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Etale cohomology can not be computed by Cech

ag.algebraic-geometry nt.number-theory cohomology etale-cohomology cech-cohomology asked Sep 23, 2016 at 22:59

mathoverflow.net

23 votes

Is the $H$-space structure on $S^7$ associative up to homotopy?

at.algebraic-topology homotopy-theory h-spaces asked Dec 3, 2016 at 22:48

mathoverflow.net

15 votes

Lower central series quotients in terms of (co)homology

ag.algebraic-geometry at.algebraic-topology gr.group-theory group-cohomology hodge-theory asked Apr 17, 2016 at 23:30

mathoverflow.net

14 votes

Local proof of Grothendieck-Riemann-Roch theorem

ag.algebraic-geometry rt.representation-theory homological-algebra lie-algebras characteristic-classes asked May 21, 2016 at 0:36

mathoverflow.net

8 votes

Functorial classes in Brauer group

ag.algebraic-geometry nt.number-theory homological-algebra etale-cohomology asked Sep 22, 2016 at 0:17

mathoverflow.net

8 votes

Grothendieck's motivation of crystalline cohomology

ag.algebraic-geometry nt.number-theory reference-request p-adic-hodge-theory crystalline-cohomology asked Sep 30, 2016 at 23:00

mathoverflow.net

8 votes

Failure of integral comparison between crystalline and de Rham cohomology over a highly ramified base

ag.algebraic-geometry nt.number-theory p-adic-hodge-theory asked Apr 15, 2018 at 19:59

mathoverflow.net

7 votes

Arbitrarily non-degenerate Hodge to de Rham spectral sequence

ag.algebraic-geometry homological-algebra hodge-theory spectral-sequences positive-characteristic asked Jan 14, 2017 at 21:33

mathoverflow.net

7 votes

Does Chabauty-Coleman method give an algorithm for finding rational points?

ag.algebraic-geometry nt.number-theory arithmetic-geometry rational-points birch-swinnerton-dyer asked Sep 11, 2016 at 15:52

mathoverflow.net

6 votes

Multiplication in universal enveloping algebra in terms of PBW isomorphism

co.combinatorics rt.representation-theory lie-groups lie-algebras asked May 30, 2016 at 23:16

mathoverflow.net

Top Answers

Crux of Dwork's proof of rationality of the zeta function?

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Commutative ring $R$ with no nontrivial idempotents, with a localization $R_r$ with infinitely many idempotents

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Question on the Sato-Tate conjecture

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Weaker version of Dwork's rationality of zeta function, what is needed to beef up into a complete proof?

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Are the Eigenvalues of the Frobenius on Crystalline cohomology bounded by degree?

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Printing omission in Mumford's "Lectures on Curves on an Algebraic Surface"

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Show that a field extension $L/K$ is separable iff the trace form is non-degenerate.

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P-adic functions on annuli

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Can we define fundamental groups functorially for non-pointed path connected topological spaces?

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Are "large enough" finite etale covers arithmetic?

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Can non-split extension be isomorphic to the split one as objects

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Bundle over $\mathbb{C}^{n}\setminus{0}$

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Pullback along Frobenius morphism

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Any hyperelliptic curve is never a complete intersection.

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Descent a representation over finite field

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Is there a version of algebraic de Rham cohomology that can be used to calculate torsion classes?

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Multiplicativity twisted Hochschild Kostant Rosenberg isomorphism

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Some basic questions on crystalline cohomology

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Defining hom spaces in the derived category as limits of hom spaces in the homotopy category

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Elementary examples of the Weil conjectures

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Dominant map from affine space implies unirationality

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Cohomological interpretation of G-equivariant line bundles

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Virtual mixed Tate motives

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Does every section of the map Gal$(\overline{k(\!(t)\!)}/k(\!(t)\!))\rightarrow$ Gal$(\overline{k}/k)$ stabilize a compatible system of roots of $t$?

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Lifting a splitting of an Abelian variety to characteristic 0

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A variant on characteristic $p$ de Rham cohomology

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Can Hodge symmetry fail if there is a lift to $W_2$ and the crystalline cohomology is torsion-free?

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Coefficients of the characteristic polynomial of the map on algebraic de Rham cohomology

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Vector bundles on adic spaces

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Does the Tate construction (defined with direct sums) have a derived interpretation?

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