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Results tagged with weil-conjectures
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user 4144
2
votes
Accepted
Pure varieties which are neither smooth nor projective
I don't know about interesting, but here are a few easy examples. Start with a cone $V\subset \mathbb{A}^n_k$. This is easily seen to be $\mathbb{A}^1$-homotopy equivalent to a point, so $H^i(\overlin …
- 35.2k
21
votes
Are there "motivic" proofs of Weil conjectures in special cases?
Of course, there's Serre's Analogues kählériens de certaines conjectures de Weil, Annals 1960, where he deduces an analogue of the Weil-Riemann hypothesis over $\mathbb{C}$ using standard facts from …
- 35.2k
7
votes
Hodge numbers of reduction mod $p$
For some explicit counterexamples to (2) and therefore also (4) again, see J. Suh,
Plurigenera of general type surfaces in mixed characteristic, Compositio (2008).
The only thing that you can say for …
- 35.2k
30
votes
Accepted
Gabber's original proof of his purity theorem
It's different, but it also uses Weil II. See
Purity for intersection cohomology after Deligne-Gabber
for my translation of the original.
- 35.2k