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Results tagged with etale-cohomology
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user 91041
for questions about etale cohomology of schemes, including foundational material and applications.
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Leray spectral sequence for étale homology
Let $X$, $Y$, $Z$ be quasi-projective varieties over an algebraically closed field $k$, $f: X \to Y$ and $g: Z \to X$ proper (even projective) maps with $f$ smooth, and $h: Z \to Y$ their composite. C …
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Zeta function of variety over positive characteristic function field vs. local zeta factor o...
Let $X = Y \times_{\mathbb{F}_q} C$, with $Y, C / \mathbb{F}_q$ smooth projective varieties, $C$ a curve. Let $d = \dim_{\mathbb{F}_q} X$. We can consider the local zeta function $Z(X, t) = \prod\limi …
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Accepted
Zeta function of variety over positive characteristic function field vs. local zeta factor o...
The two zeta functions are the same. This is an immediate corollary of Milne, Etale Cohomology, proposition 13.8(c).
Reference:
Milne, J. S. Etale Cohomology (PMS-33). Princeton University Press, 1980 …
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Deligne finitude and finiteness of etale cohomology
See the answers here: https://mathoverflow.net/questions/76069/finiteness-of-étale-cohomology-groups . Because $k$ is finite, a constructible sheaf on (Spec $k)_{et}$ has finite cohomology groups. Del …
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