At five o'clock I am standing outside the front steps of the National Museum. It is almost dusk, and the streetlights have come on above heavily wrapped pedestrians scurrying against gusts of a bitter east wind. The last tourist boats are returning to their berths in front of the Grand Hotel and a Baltic cruise liner is moving slowly out across the darkening water. I feel lonely and far from help.

"Matt? h.e.l.lo, I am Dirch." I turn to see a very tall man with a severe, bony face surmounted by a crop of pale blonde hair. He peels off a black leather glove and offers his hand, which I shake cautiously. His face splits in a wide smile. "You see, we are friends. And you have the book?" He nods at my backpack.

"Yes."

"Good, follow me."

He leads the way to one of the piers jutting out into the water, and I see a powerful motor launch waiting there with a man in a skipper's cap at the wheel. We climb aboard and roar away across the bay. Gradually the s.p.a.ces between the islands become wider and the lights of the suburbs more distant, until, as night closes in, they become isolated points in the dark. The water becomes rougher, the wind sharper as we bounce out of sheltered waters into the Baltic. I bow my head against the freezing spray and cling to the rail of the boat and try not to think the worst.

After half an hour the boat swings suddenly to port and throttles down, and I see the flash of a navigation buoy ahead. The captain speaks into a radio, and lights appear in the darkness, illuminating a jetty. The two men help me up onto the timber decking, and Dirch and I walk towards the land, a dark ma.s.s of foliage and rock.

"Welcome to Blod o," he says softly. I smell the brine of the sea mixed with the decay of autumn foliage.

A black 4WD is waiting for us, and I recognize the driver as one of the two skinheads who attacked me in Gamla Stan. He gives me an ugly smile as we get in. It's hard to make out much more than tree trunks and rocks in the headlights as we climb up a steep hillside. Then the view opens out to a large mansion with a portico of cla.s.sical columns framing a front door at which we pull to a halt. Inside a uniformed manservant takes my coat and cap, but I hang on to my bag.

Dirch leads me to a sitting room, where a log fire is blazing in a hearth. He offers me something to warm me up, coffee or something stronger, but I decline, saying I just want to see my sister. He nods gravely and says he will arrange it and leaves. I wait by the fire, trying to thaw the chill in my bones, and then the door opens and Abbie comes in and we rush to each other and hug with relief.

I think how haggard and disoriented she looks, and I wonder if they have been giving her drugs. We sit in front of the fire and clutch each other's hands and I ask her if they've hurt her.

"I'm all right, Matt, really."

"You don't look well, sis."

"It's nothing, just lack of sleep. They won't let me sleep, you see. It's their way of making me come to terms. It's amazing how obliging you become after a few days without sleep. But I'll be all right now. You've brought the book?"

"Yes, but how do we know they'll let us go after we give it to them?"

"They don't want to keep us here. We have agreed a price, and once they have the drawing they will pay me and we can leave."

"How much?"

"Fifty thousand."

"But it's worth millions!"

"It's enough, Matt. I just want this to be over."

"What about Rich? Is he here?"

"Yes, we spoke when he first arrived." Abbie frowns. "He became angry and said I shouldn't agree to their terms, and they took him away and I haven't seen him since. But they've promised to let him leave with us."

I don't like the sound of this, but there's not much I can do, and as if he's been listening to our conversation, which he no doubt has, Dirch opens the door and says, "Well now, we will conclude our business and let you go home to your nice warm beds."

"Will we meet Mr Graven?" I ask.

"Of course. He is most anxious to be present at the final transaction. Follow me."

I don't much like the sound of final transaction, but we do as he says, me taking Abbie's arm when she seems unsteady on her feet, b.u.mping into the doorway.

He leads us along a corridor and down a staircase into the bas.e.m.e.nt, very different in character from the upper floor, with clinical white walls and fluorescent light fittings, like a laboratory or a morgue. Dirch opens a door for us into a large room lined with workbenches on which a variety of high-tech equipment is set out computers, special lamps, and an elaborate microscope. A man in a white coat looks up from a keyboard and comes towards us.

"What is this place?" I ask.

"This is Mr Graven's art conservation laboratory," Dirch says. "We shall be able to examine your drawing under perfect conditions here. Ah ..."

We turn to see Rich being pushed roughly into the room by the two skinheads. He looks terrible, his face swollen and bruised, one eye completely closed, his hands cuffed in front of him. He gives me a wry grin and a wink with his good eye.

A pair of double doors on the far side of the conservation room open and the manservant comes in pushing a wheelchair in which sits the hunched figure of an old man with a tartan rug spread across his knees. The pair come to a stop and the seated man peers up at me intently. It is an unsettling experience, as if he is trying to look inside my head. The two sides of his face don't quite match, and I guess he has had a stroke.

Dirch goes to the seated man and bows to hear him murmur something in a hoa.r.s.e whisper. Dirch nods and turns to us. "Mr Graven is impatient to view your merchandise. Shall we proceed?"

The man in the laboratory coat draws on a pair of white gloves and comes towards us. I open my backpack and give the book to Abbie, who lays it on the bench in front of us and opens it at the back cover.

"The drawing is inside a protective envelope beneath the lining of the cover."

She indicates to the technician, who runs his fingers across the surface, feeling for the extra thickness beneath. He nods and fetches a scalpel and tweezers, and begins delicately peeling back the lining. We are all focused on his work, holding our breath as the white envelope is revealed. When it is free he picks it up carefully and carries it reverently across to Martin Graven, whose divided face has taken on a greedy, predatory look, and pulls a trolley out from beneath a bench and positions it in front of Graven, then places the envelope on the surface, opens its flap with the tweezers, and slowly slides out the contents. For a moment no one speaks, then everyone starts talking at once. With a shock I recognize the thing lying there on the trolley, and it isn't a Leonardo self-portrait. It is the cover of a paperback book, The Girl with the Dragon Tattoo.

As the cries of consternation and anger die away, everyone turns to stare at me. I'm speechless.

Then Graven spits a stream of Swedish at Dirch. Graven has gone pale, trembling with anger. He gives us one last furious glare and the manservant wheels him around and propels him out of the room. Dirch is speaking to someone behind us, and we turn to see the two skinhead thugs standing there. They grab hold of Rich and me and drag us out into the corridor, followed by Dirch and Abbie. Abbie is calling to me, a desperate cry, "Matt, what have you done?" We are bundled into another room, where Rich and Abbie are pushed on to steel chairs against the wall. A third chair is dragged out into the middle of the room and I am shoved down hard on to it. One of the skinheads stands with Rich and Abbie while Dirch and the other confront me.

"Now," Dirch says, "you will kindly explain."

I watch the thug at his side pull a set of bra.s.s knuckle-dusters out of his pocket and fit them to his large right fist, and I quickly begin talking.

"After I got away from these two at the changing of the guard, I ran into an antiquarian bookshop and hid the book on a shelf there."

"Yes," Dirch nods, "we worked that out."

"You killed the owner, didn't you?"

He waves his hand impatiently. "Get on with it."

"The next day I returned to retrieve the book and found the police there. I spoke to one of the shop a.s.sistants, who told me she had sold the book to a regular customer, and gave me her address. I went to see her, and told her the whole story, about the Leonardo drawing and everything."

"What?" Abbie cries in disbelief.

"I thought she seemed trustworthy, and I had no one else I could turn to for help," I continue desperately. "She warned me that Martin Graven was a very dangerous man, and I agreed to leave the book with her until I knew what was happening. She must have opened the lining and taken the drawing."

I hear Rich give a groan, and Abbie sobs, "Matt, how could you be so stupid!"

"Be silent!" Dirch snaps.

I can see from the dark scowl on his face that Dirch is having difficulty believing my story.

"It's true, I swear."

"So, who is this woman, what does she look like?"

"She looks ... exactly like the face on the front of that book cover Lisbeth Salander. Her name is Vera Kulla, and she lives in an apartment on Fiskargatan, on Sodermalm."

Dirch draws back, his face stony, and when he speaks his voice is ominously quiet. "You must think we are very stupid. In the second book of the Millennium Trilogy, The Girl Who Played with Fire, Lisbeth Salander bought an apartment in Fiskargatan ..."

"Yes," I stammer, "I know, but ..."

He cuts me off. "She bought it using an a.s.sumed name V. Kulla."

I'm stunned. "I ... I didn't remember that ..."

He shakes his head sadly. "You are determined to make things difficult for yourself, Matt. Do you think you are a tough guy, eh? Did you think you would impress your sister? Why don't you tell him, Abbie, tell your idiotic young brother to stop playing these games."

"Yes," Abbie sobs. "Matt, please, this is madness. Tell him where the Leonardo is!"

"She must have it," I whisper, "Vera Kulla ..."

Dirch gives a grunt of disgust and turns to the skinhead with the bra.s.s knuckles and gives him a nod. The man draws back his fist and I close my eyes.

There is a sudden commotion, a crash, I open my eyes again and see Rich on his feet, gripping his steel chair like a club and swinging it at the men who are stumbling away from him. "Run!" he cries, "Run!" and I realize he's talking to me. I leap to my feet and shove past the startled Dirch and dive for the door, out into the corridor, turn right, run, then skid to a halt as the manservant appears at the corner ahead of me. I turn back but Bra.s.s Knuckles is out now and coming for me. Then a door in front of me opens and the technician peers out, wondering what the commotion is. I shove him back inside and follow, locking the door behind me, and stand there gasping, looking around me.

This is a different room, dark walls, ceiling and floor, subdued pools of light focused on a series of images hanging on the walls. It is an art gallery, I realize, Martin Graven's private collection, and one of the paintings catches my eye. I have seen it before, in an art book, a portrait of a young man with extraordinarily long arms and a red waistcoat, rendered in the broken brushstrokes of Cezanne. Looking around the room I see other paintings which, although I don't recognize them, are in the style of famous artists a Rembrandt over there, a Pica.s.so surely, and doesn't that look like a Vermeer?

My attention is interrupted by banging on the door, the handle being rattled. I look around, my eyes becoming used to the dim light, and I realize that there is no other exit.

The technician has backed away, staring at me with wide nervous eyes. Then a voice sounds over some kind of intercom. I recognize Dirch.

"Matt, you are being very stupid. Open this door at once."

"No," I call back loudly. "I don't think so."

"That room is equipped with a fire suppression system that sucks out all the oxygen and floods the s.p.a.ce with carbon dioxide. If you do not open the door I will activate it and you will be suffocated."

The technician looks alarmed and calls out, "No, no! Nej! Behaga!"

I notice that he still has his instruments in the top pocket of his coat, and I leap at him and s.n.a.t.c.h the scalpel. I call out to the invisible speaker, "Please don't do that, Dirch. Your conservator here would be very upset, and so would I. And I have his scalpel, and before I die I'll slice the Cezanne to ribbons, and as many of the others as I can, too."

There is a lengthy silence during which I try to work out what my options are. It feels as if I'm playing chess with just one p.a.w.n left and my opponent with all his pieces intact. Finally I walk across the room to the Cezanne and say to the technician, "All right, open the door."

He does it, and Dirch is standing there flanked by his two heavies. I raise the blade of the technician's scalpel to the surface of the painting and tell Dirch to get Abbie and Rich. He makes a move forward, into the room, and I jab the tip of the blade into the canvas. He gives a horrified gasp and hesitates.

"Do as I say, Dirch."

He turns abruptly and whispers to the skinheads, who disappear. In a moment they return with the other two. One of the men hands Dirch something and he grabs hold of Abbie's hair and pulls her into the room.

"Well now, Matt," Dirch says. He is trying to remain calm, but he is breathing very heavily. "Here is Abbie, and here ..." he lifts up his hand "... is my scalpel." He presses it to Abbie's throat. "Now let us examine the logic of this situation. If you do not surrender I will cut your sister's throat. What good will it do you then to damage that painting? Which is more valuable, the painting or your sister? Now be a sensible fellow."

He nods one of the skinheads forward, and there is nothing I can do. I hand him the knife and he takes it carefully and then slams his fist hard into my stomach. I double up in agony and through the pain I hear Dirch say, "We could have so easily done a deal. But now, thanks to your stupidity, that is impossible." Then the skinhead hits me again, and again. I pa.s.s out to the sound of Abbie screaming.

I come round to find that we are slumped together on the floor of a small room, like a prison cell. They have obviously roughed Rich up some more and he looks as bad as I feel.

"Are you all right, Matt?" Abbie whispers.

I mumble a yes. Trying to clear my brain, I remember the last words I heard. "What did he mean, that it's impossible now to do a deal?"

"Because we saw the paintings," Abbie says. She sounds exhausted and resigned.

"What do you mean?"

"The Cezanne Boy in a Red Vest was stolen from a gallery in Switzerland in 2008. The Rembrandt seascape, the only one that he ever painted, was taken from a Boston museum in 1990, along with the Vermeer, which is reckoned to be the most valuable painting that has ever been stolen. And it's the same for all the others they're all masterpieces that have been taken during the past twenty years and never been traced. He can't let us go now that we've seen them here."

I groan. "What do you think they'll do with us?"

By way of reply, the door opens and Dirch comes in. "There is a 200-metre deep trench in the floor of the Baltic Sea some fifty kilometres south of here," he says. "Many unwanted things end up down there. Come, it is time to go."

We are hauled roughly to our feet and marched up a flight of stairs and out into the cold night air, hands manacled. They lead us across a gravel yard and we pa.s.s a truck being loaded with heavy concrete weights, each with a chain attached. We reach a path that descends steeply through woods towards the m.u.f.fled roar of the sea breaking on a rocky sh.o.r.e. When we reach the foot we see their boat tied up against the jetty. The skinheads prod us forward, and we obey, shuffling like sheep to the slaughter. Then something comes out of the darkness from the trees to our right. I catch only a glimpse of it before the first skinhead drops to his knees with a strangled cry and falls flat on his face. The second whirls around and there is a sudden crackling noise and he too gives a scream and falls, and I see Vera Kulla standing behind him with a Taser gun in her hands.

"Come on," she says urgently, and begins running across the rocks into the trees. Behind us on the path, Dirch, who was bringing up the rear, has retreated and is shouting back up the hill for help. We rush after Vera with our bound hands and come to the small dinghy she has pulled in among the rocks. In silent panic we slip and stumble across the wet boulders and fall into the boat and she starts the outboard and we set off.

It is a tiny boat, and with four of us in it the choppy waves spill over the side and drench us. For several minutes we are alone in the darkness, sawing at our ropes with a knife Vera gives us, but then we see a beam of light to our stern, searching for us. Being so low in the water saves us for a while, and the light veers away to starboard, then swings around, sweeping, probing, until finally it catches us. We look back like dazzled rabbits as it fixes on us and grows brighter as their more powerful boat narrows the distance; all except Vera, I notice, who is staring fixedly ahead. I turn to see what she is staring at, and make out a great shoal of rocks and reefs jutting out of the water ahead, picked out by the spotlight. I remember seeing all this from the air as I flew into Stockholm, the sea scattered with thousands of tiny islands and outcrops of rock.

Vera heads straight for it without slowing down and I grip the side of the boat tight with numb fingers, certain that we will crash at any moment. Now we're into the shoals, swinging wildly from side to side as jagged rocks jump out of the darkness ahead of us. Again and again the aluminium hull sc.r.a.pes and thumps against outcrops, the engine howling. After ten heart-stopping minutes of this, Vera abruptly throttles back. I realize that the light from the pursuing boat is less bright, and keeps losing track of us. "They're not coming into the rocks?" I ask Vera, and she nods grimly. She weaves the boat more slowly, further and further into the shoal, the visibility almost nil as the light behind us fades. For perhaps an hour we move cautiously through the maze, until finally the stretches of water become more open, and I notice a glow of light in the sky up ahead Stockholm! It is another hour before Vera reaches the city and tucks the boat into a mooring between dozens of others and, shaking with cold and cramp, we climb ash.o.r.e. We are at the western end of Sodermalm Island, she tells us, about three kilometres from the city centre to the north, and the same distance to the apartment in the eastern part of Sodermalm where I visited her.

"I have a friend here who will shelter you for tonight. It isn't safe for you in Stockholm. Graven's people will be searching for you. What's wrong?"

She says this to Abbie, who is staring at her, seeing her in the light for the first time. "You do look like Lisbeth Salander," Abbie says.

Vera shakes her head impatiently. "Tomorrow you must leave."

"Yes," Abbie agrees. "We'll catch a flight to London."

"Not from Stockholm, they'll be watching for you at the airport and the Central Station. First thing tomorrow my friend will drive you down to Helsingborg, where you can cross over to Denmark, and catch a plane or a train back to England from Copenhagen."

She has brought us to the door of a small house, where there are three doorbells. She rings one of them and an Asian girl answers. "This is my friend Miriam," Vera says, and says something to her friend in Swedish. Miriam gives us a big smile and we stagger thankfully into a small apartment, blissfully warm and welcoming.

One by one we have hot showers, and Miriam dresses our wounds and gives us hot soup. Abbie is so exhausted after having had only brief s.n.a.t.c.hes of sleep for a week now that she immediately falls into a deep slumber in an armchair. Rich and I talk to Vera for a while until we too are overcome with exhaustion. Rich asks her if she will inform the police about Graven and his collection of stolen paintings, but she shakes her head. "There's no point," she says. "Even if the police agree to get a warrant they will find nothing. One day Martin Graven will face his punishment, but not over this." There seems something personal in the way she says this, but she refuses to elaborate. Rich nods and closes his eyes and soon he too falls asleep.

Then I say, "I have to thank you for saving our lives, Vera. But you put us in danger in the first place, by removing the Leonardo drawing."

"No, Matt. You did that by insisting on taking the book to Blood Island. Graven was never going to let any of you go free, it was too risky for him. All I could do was follow you out there and wait for my chance."

I feel very naive and tell her so, thanking her again.

"Actually it's your sister and Rich who were naive," she says. "Very naive to think they could negotiate with Graven. They should have known Rich especially that such a man doesn't negotiate with people like us, he just gobbles us up."

"So, the Leonardo?" I say.

"Ah yes, the Leonardo ..."