Witt vector cohomology

In mathematics, Witt vector cohomology was an early "p"-adic cohomology theory for algebraic varieties introduced by . Serre constructed it by defining a sheaf of truncated Witt rings "W""n" over a variety "V" and then taking the inverse limit of the sheaf cohomology groups "H""i"("V", "W""n") of these sheaves. Serre observed that though it gives cohomology groups over a field of characteristic 0, it cannot be a Weil cohomology theory because the cohomology groups vanish when "i" > dim("V"). For Abelian varieties showed that one could obtain a reasonable first cohomology group by taking the direct sum of the Witt vector cohomology and the Tate module of the Picard variety.