The late Swedish author Steig Larsson created a series of books originally titled “Men Who Hate Women” with a character who was an idealized version of himself — an investigative journalist of impeccable integrity and political correctness who effortlessly appeals to women.  But it was the other lead character in the books who inspired the final titles of the trilogy and who became an international sensation, the dragon-tattooed bisexual computer wizard Lisbeth Salanger, a ward of the state for her violent behavior and anti-social demeanor, with no respect for conventional rules but with a passionate commitment to justice.  “She’s different,” says her employer. “In what way?” “In every way.”

The three books inspired three excellent Swedish films with Noomi Rapace as Lisbeth, and now David Fincher (“Se7en,” “Zodiac,” “The Social Network”) has taken the helm of a big-budget American remake, with Daniel Craig as journalist Mikael Blomkvist and Rooney Mara (briefly glimpsed in “The Social Network” as the girl who breaks up with Mark Zuckerberg in the first scene) as Lisbeth.

Fincher’s version is very true to the book, sharing its strengths and its weaknesses.  Mara’s version is slightly softer than Rapace’s, she still delivers the character’s most intriguing qualities, the combination of blatant punk style with a resolutely inaccessible core, her combination of vulnerability and resilience, her determination, and, above all, her ability to triumph over the most horrifying violations.  As the original title suggests, the weakness of the story is Larsson’s clunky insistence on including every possible form of atrocity, and those who are familiar with the plot may find that there are not enough surprises left.  A superb soundtrack by Atticus Ross and Trent Reznor (who also did “The Social Network”) is interrupted by a jarring version of Led Zeppelin’s “Immigrant Song.”

It begins with a scene that could have come from Raymond Chandler.  Mikael, discredited following a libel suit by a powerful businessman, is invited to meet with an even more powerful figure, Henrik Vanger (Christopher Plummer), the head of one of Sweden’s wealthiest families.  In his huge home in a island that serves as a family compound, Henrik explains that he is haunted by the disappearance of his young granddaughter Harriet  forty years before.  Each year, on his birthday, Vanger received a pressed flower, a symbol of his relationship with Harriet that he believes comes from her killer and is intended to taunt him.  The police and private detectives have tried to find out what happened to Harriet but the mystery is still unsolved.  No body has been found and there seems to have been no way for her to leave the island.  Mikael agrees to see if he can find out what happened.  “You will be investigating thieves, misers, and bullies,” Henrik tells him, “the most detestable collection of people you will ever meet — my family.”

What Mikael does not know is that he has already been investigated by Henrik, whose aide hired a firm to do a background check.  The research was done by Lisbeth Salanger, who hacked into Mikael’s email and has done a very thorough, if not strictly legal, analysis.  The only person Lisbeth trusts, her state-appointed guardian, has a stroke and his replacement is an abusive monster who insists on sexual favors before allowing her to have access to her money.  After some horrifying encounters, Lisbeth extracts some revenge.  Meanwhile, Mikael makes some progress but realizes he needs help.  The aide suggests Lisbeth, and so our two protagonists meet.

Steven Zallian (“Schindler’s List,” co-screenwriter of “Moneyball”) adapted the book well, discarding some distracting subplots.  The soundtrack and production designer Donald Graham Burt superbly convey the frozen remoteness of the setting.  Mikael is not easy to portray because he spends a lot of time watching and listening but Craig makes Mikael thoughtful and lets us see that he recognizes his failures.  Mara’s voice is a little too sweet for Lisbeth but her efficient, straightforward physicality and her watchful but implacable expression are just right for the character who is about to kick the hornet’s nest.

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