Witt Vector Cohomology

(Algebraic Geometry)

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Algebraic Geometry
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What is Witt vector cohomology?

In mathematics, Witt vector cohomology was an early p-adic cohomology theory for algebraic varieties introduced by Serre . Serre constructed it by defining a sheaf of truncated Witt rings Wn over a variety V and then taking the inverse limit of the sheaf cohomology groups Hi(V, Wn) 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.

Technology Types

algebraic geometrycohomology theory

Synonyms

Serre's Witt vector cohomologyWitt cohomology

Tech Info


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