- Source: Witt vector cohomology
In mathematics, Witt vector cohomology was an early p-adic cohomology theory for algebraic varieties introduced by Serre (1958). 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, Serre (1958b) 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
Serre, J.P. (1958), "Sur la topologie des variétés algébriques en caractéristique p", 1958 Symposium internacional de topología algebraica, Mexico City: Universidad Nacional Autónoma de México and UNESCO, pp. 24–53, MR 0098097
Serre, Jean-Pierre (1958b), "Quelques propriétés des variétés abéliennes en caractéristique p", Amer. J. Math., 80: 715–739, doi:10.2307/2372780, MR 0098100
Kata Kunci Pencarian:
- Witt vector cohomology
- List of things named after Ernst Witt
- P-adic cohomology
- Crystalline cohomology
- Artin–Schreier theory
- Rigid cohomology
- BRST quantization
- Kähler differential
- Étale cohomology
- Exterior algebra
