The shimura-varieties tag has no wiki summary.

**3**

votes

**0**answers

460 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 ...

**4**

votes

**0**answers

176 views

### vanishing of automorphic bundles

Let $S _K = S_K(G,X)$ be a Shimura variety of dimension $n$. Let $\xi$ be a (finite-dimensional) representation of $G$, which gives rise (by a construction of Harris) to an automorphic bundle $V(\xi)$ ...

**0**

votes

**0**answers

353 views

### higher direct image, Shimura varieties of PEL-type and representations

Let $M=M(G,X) = (M_K)_K$ be a Shimura variety of PEL-type associated to datum $(G,X)$. Let $A$ be the universal abelian scheme over $M(G,X)$ and $a: A \rightarrow M$.
Now, using notations from ...

**5**

votes

**1**answer

630 views

### Are all Shimura Varieties Special Subvarieties of the Siegel modular Variety?

Given a Shimura variety $S$, is it possible to imbed $S$ as a special Subvariety
of the Siegel modular variety $A_{g,N}$, for some $g$ and level $N$? I expect that the answer is yes, essentially since ...

**5**

votes

**1**answer

432 views

### different Shimura data with common underlying group?

A pure Shimura datum is of the form $(G,X)$ with $G$ a connected reductive $\mathbb{Q}$-group, and $X$ a homogeneous space under $G(\mathbb{R})$, subject to Deligne's conditions in terms of Hodge ...

**5**

votes

**1**answer

774 views

### Generalizing Eichler-Shimura to higher dimension, again

This question is related to
Intuition behind the Eichler-Shimura relation?
and
L-functions and higher-dimensional Eichler-Shimura relation
Answering the first question above, Matt Emerton gives a ...

**31**

votes

**3**answers

1k views

### Are there motives which do not, or should not, show up in the cohomology of any Shimura variety?

Let $F$ be a real quadratic field and let $E/F$ be an elliptic curve with conductor 1 (i.e. with good reduction everywhere; these things can and do exist) (perhaps also I should assume E has no CM, ...

**13**

votes

**3**answers

1k views

### Constructing coherent sheaves on Shimura varieties.

Let me first run through the setting of my question in an example I understand well; that of modular curves. If $Y_1(N)$ denotes the usual modular curve over the complexes, the quotient of the upper ...

**6**

votes

**2**answers

833 views

### modularity of algebraic varieties

Hello,
Are there any examples of varieties which are not Shimura varieties or abelian varieties
and whose L-functions have been shown to be a product of automorphic L-functions?
Thanks.
N

**3**

votes

**1**answer

436 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 ...