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 In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space. Broadly speaking, sheaf cohomology describes the obstructions to solving a geometric problem globally when i ...
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.
References
*
*{{citation, mr=0098100
, last=Serre, first= Jean-Pierre
, title=Quelques propriétés des variétés abéliennes en caractéristique p
, journal=Amer. J. Math. , volume=80, year= 1958b , pages=715–739, doi=10.2307/2372780
Algebraic geometry
Cohomology theories