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Results tagged with shimura-varieties
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user 2284
5
votes
1
answer
590
views
What is the image of complex conjugation under Siegel Galois representations?
Let $G$ be the reductive group $\operatorname{GSp}_{4}$. Let $\pi$ be a smooth admissible cuspidal representation of $\operatorname{GSp}_{4}(\mathbb{A}^{(\infty)})$ of dominant weight. Assume, for cau …
- 10.9k
4
votes
Are there motives which do not, or should not, show up in the cohomology of any Shimura vari...
Let me expand and hopefully clarify my first comment about the more specific question of whether the cohomology of a modular elliptic curve with everywhere good reduction shows up in the cohomology of …
- 10.9k
4
votes
Are there motives which do not, or should not, show up in the cohomology of any Shimura vari...
In their 2017 preprint
On subquotients of the étale cohomology of Shimura varieties
C.Johannsson and J.Thorne have made substantial progresses towards question 4. In particular, they show that under …
- 10.9k
5
votes
Accepted
Matsushima-Murakami Isomorphism for $L^2$-cohomology
Morally yes, by
Franke, Jens Harmonic analysis in weighted $L_{2}$-spaces. Ann. Sci. École Norm. Sup. (4) 31 (1998), no. 2, 181--279
See especially theorem 4 (and note that if you want an equivarian …
- 10.9k