All Questions
Tagged with shimura-varieties galois-representations
9 questions
1
vote
0
answers
255
views
Why does Deligne's construction of the Galois representation attached to the new cuspidal forms require that the Kuga-Sato manifold be regular?
The origin of this question is related to the construction of Galois representations of Deligne attached to $f$ a new cuspidal form (of weight $k\geq 2$). To do this, we consider the fiber product $k$-...
- 1,270
21
votes
1
answer
2k
views
Cohomology of Shimura varieties and coherent sheaves on the stack of Langlands parameters
In Zhu's Coherent sheaves on the stack of Langlands parameters theorem 4.7.1 relates the cohomology of the moduli stack of shtukas to global sections of a certain sheaf on the stack of global ...
- 3,309
8
votes
1
answer
552
views
Artin reciprocity via Shimura varieties
The point of Shimura varieties, as far as I've understood it, is that for a given Shimura datum $(G,D)$, there exist models, by which I mean that for congruence subgroups $\Gamma$ there exists a ...
- 4,418
7
votes
0
answers
450
views
Galois representations in cohomology of quaternion Shimura varieties
Let $F$ be a totally real field, and $E \subseteq F$ a subfield. Choose a quaternion algebra $B$ over $F$ satisfying the following condition:
there is a distinguished infinite place $\tau$ of $E$ ...
- 37k
9
votes
0
answers
656
views
Langlands program beyond CM fields?
I apologize since this is a quite vague question. And I am personally at an expert in these fields at all.
It seems to me that there are two main directions of the Langlands program, namely, ...
- 91
4
votes
1
answer
394
views
semisimplicity of automorphic Galois representations
Is it known that the Galois representation constructed by Harris and Taylor in their book is semisimple? I can't see this proven in the book, but on the other hand, everywhere else the representation ...
- 2,842
8
votes
1
answer
1k
views
Is the Galois x Hecke action on cohomology of Shimura varieties semi-simple?
Given a reductive group $G/\mathbf Q$ (+ additional data), and a compact open subgroup $K\subset G(\mathbf A^\infty)$, there is a standard construction that produces a Shimura variety $S$ and if we ...
- 647
5
votes
0
answers
672
views
choice of local system in Deligne's construction of $l$-adic Galois representations
Hello,
Deligne famously constructed $l$-adic representations of $G_\mathbf Q = Gal(\overline{\mathbf Q}/\mathbf Q)$ starting form cusp modular forms of weight $k$ by looking inside the cohomology ...
- 2,842
5
votes
1
answer
596
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 ...
- 10.9k