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Results tagged with etale-cohomology
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user 1384
for questions about etale cohomology of schemes, including foundational material and applications.
13
votes
1
answer
1k
views
Analogue of Shimura curves in the symplectic case?
My understanding is this: one can attach 2-d Galois representations to classical modular eigenforms because one can look in the etale cohomology of modular curves. For Hilbert modular forms the naive …
- 41.4k
19
votes
6
answers
2k
views
weight 4 eigenforms with rational coefficients---is it reasonable to expect they all come fr...
A weight 2 modular form which happens to be a normalised cuspidal eigenform with rational coefficients has a natural geometric avatar---namely an elliptic curve over the rationals. It seems to be a su …
- 41.4k
124
votes
Accepted
Etale cohomology -- Why study it?
$\DeclareMathOperator{\gal}{Gal}$
Here's a comment which one can make to differential geometers which at least explains what etale cohomology "does". Given an algebraic variety over the reals, say a s …
- 41.4k
5
votes
Quotients of Tate modules
Although this question isn't really well-defined (you'd surely need to be more precise about the word "canonical" in the comment under the question) let me make two comments which hopefully put this t …
- 41.4k
31
votes
Intuition behind the Eichler-Shimura relation?
Let me highlight some issues that Emerton doesn't:
1) you seem to hint that you don't know that modular forms can be viewed as a product of a bunch of local terms. So there is an adelic story, where …
- 41.4k