Girl With the Dragon Tattoo is a beautiful thriller

Rest assured, Stieg Larsson acolytes. One of the most important questions to be asked in the late Swedish author's mega-selling mystery The Girl With the Dragon Tattoo - the line "Do you want a coffee?" - makes it into David Fincher's movie.

In fact, this beautifully taut and terrifying thriller is faithful to its source in just about every way that matters. Perhaps the opening title sequence - a kind of Mapplethorpe-meets-Bond S&M whir set to Karen O's urgent take of Led Zeppelin's "Immigrant Song" - is too much. But, like all those signature 007 openings, this one has the feel of a franchise about it, so there have to be two sequels now, right? (Maybe three, if the hard drive on Larsson's laptop has anything to say about it.)

Set in Stockholm, and on the frozen island of Hedeby, with its cluster of grand estates and quirky cottages belonging to the rich and totally messed-up Vanger clan, The Girl With the Dragon Tattoo digs its mitts into the twisted matter of Larsson's elaborate whodunit. And it introduces a formidable talent - Rooney Mara, whom Fincher gave a small role in The Social Network (as the girl who dumps Facebook founder Mark Zuckerberg). Mara, pierced and punked-out, is Lisbeth Salander, the asocial, bisexual genius hacker and misfit - one of the great heroines of detective fiction, as different from Miss Marple as a toot of crank is to a nice cup of tea.

If you've seen the Swedish film adaptations of the Millennium Trilogy and thought no one could inhabit Lisbeth like their star, Noomi Rapace, well, think again. Mara nails this damaged, determined soul - you can see it in her quick, sad eyes, in the cool but nervous manner by which she takes everything in. Lisbeth's rage, her pain, her intelligence - it's all here.

And speaking of James Bond, Daniel Craig sheds the suave Her Majesty's Secret Service airs to play Mikael Blomkvist. The intrepid investigative reporter has landed himself in a libel suit - publishing an apparently erroneous expose of a Swedish tycoon - thereby bringing shame on himself and his magazine, Millennium, and its publisher, Erika Berger (Robin Wright), who also happens to be his lover, even though she is married and her husband is all right with that. (Hey, hey, it's Sweden!) Craig brings a bookish verve to his performance, doing this weird thing with his eyeglasses, letting them dangle from one ear as he pores over problematic pieces of evidence.

And on the off-chance that The Girl With the Dragon Tattoo is new to you, the case that he - and then Lisbeth, too - is investigating revolves around the disappearance from Hedeby, four decades earlier, of a teenage girl, one of the moneyed Vanger brood. It is Henrik Vanger (Christopher Plummer), the aging Swedish industrialist (and the girl's great-uncle), who asks Blomkvist to look into what he believes to be a murder.

And as Blomkvist and Salander poke around, it is the serial murders of many, many women that they uncover. The Girl With the Dragon Tattoo is very much about evil - evil rooted in family, in national identity, and evil that manifests itself in sexual abuse and misogyny. Never forget: The original Swedish title for Larsson's book was Men Who Hate Women.

Fincher, who has explored the psychology and pathology of serial killers in both Seven and Zodiac, is in absolute control here, even when things veer out of control for his protagonists. The rape scenes - there are two, one with Lisbeth as victim, one as avenger - are unrelentingly graphic, but not for a second are they exploitive.

(Fincher and Steven Zaillian, the screenwriter, have eliminated some of the book's more tangled subplots, and made one change that, while significant, doesn't compromise the integrity or purpose of Larsson's story.)

And there's a wonderful sense of place in this film, too: the sleek cafes and architecture of Stockholm, the cold majesty of the provinces to the north, the houses with their bright-colored doors.

The Girl With the Dragon Tattoo is long, but doesn't feel so. In fact, toward the end, it feels unnecessarily hurried, as mysteries are resolved, and as Lisbeth Salander and Mikael Blomkvist start to look like an item - the middle-aged journo and the young cyber-sleuth who has saved him, as he has saved her.

On to The Girl Who Played With Fire, please!