All Questions
15 questions with no upvoted or accepted answers
17
votes
0
answers
1k
views
Katz--Mazur for abelian varieties
Over $\mathbb Z$, there is a smooth DM stack $A_g$ classifying abelian varieties.
Over $\mathbb Z[\frac 1N]$, there is finite etale cover $A_g(N)_{\mathbb Z[\frac 1N]}\to A_g\otimes\mathbb Z[\frac 1N]...
- 18.7k
11
votes
0
answers
264
views
What is the lowest-weight non-cyclotomic Galois representation in $\overline{\mathcal M}_{g,n}$?
I want to know about low-weight Galois representations in $H^i(\overline{\mathcal M}_{g,n}, \overline{\mathbb Q}_\ell)$ that aren't cyclotomic. This should be equivalent to finding $p,q$ such that $H^{...
- 148k
9
votes
0
answers
194
views
Methods to compute the Kodaira dimension of moduli spaces
It is known that the moduli space $\bar{M_g}$ of genus $g$ stable curves over $\mathbb C$ is of general type for $g \geq 24$ with Kodaira dimension $3g-3=\dim \bar{M_g}$.
The idea is that one can ...
- 461
9
votes
0
answers
649
views
Motivic fundamental group of the moduli space of curves?
Suppose I have a smooth projective family of varieties of varieties over $\mathcal M_g$ - i.e. a universal functor, commuting with deformations, from curves to smooth projective varieties. Can I ...
- 148k
8
votes
0
answers
174
views
Geometry of moduli problem in practice: how to check it is connected / irreducible / normal / reduced / locally complete interesection...?
Moduli spaces are very common and useful in the world of algebraic geometry. From the point view of functors, one can already check many geoemtric properties of it. I like examples, and you can assume ...
- 461
6
votes
0
answers
590
views
Affine GIT quotients and the excursion algebra in Fargues–Scholze
Some background:
Let us fix a non-archimedean local field $E$ with residue characteristic $p$, and let $G$ be some connected reductive group over $E$. In [FS, §VIII.1.1] the authors define a moduli ...
- 777
5
votes
0
answers
327
views
Is there a concrete way to show the existence of canonical model for non-modular Shimura curves?
I am trying to read Carayol's article on the construction of Galois representations associated to Hilbert modular forms (http://archive.numdam.org/article/CM_1986__59_2_151_0.pdf). The main geometric ...
- 2,842
5
votes
0
answers
522
views
Moduli interpretation of Hecke operators on Shimura curves
In his book on Automorphic Forms, Shimura gives (chapter 9) definitions of the the Hecke operators for Shimura curves.
One can give definitions of the Hecke and Atkin-Lehner operators in terms of the ...
- 3,555
4
votes
0
answers
195
views
lemma II.2.4 in Harris-Taylor (about drinfeld-katz-mazur level structure on 1-dimensional $p$-divisible groups)
Lemma II.2.4 on page 82 in Harris and Taylor's "The Geometry and Cohomology of Some Simple Shimura Varieties" (or lemma 3.2 here), says that given a Drinfeld(-Katz-Mazur) level structure $\alpha:(p^{-...
- 371
4
votes
0
answers
1k
views
level structures and moduli of abelian varieties
Hello,
In the definition of level structure of level $n$ for an elliptic curve $A$, there are two versions:
an isomorphism of group schemes $(\mathbf Z/n\mathbf Z)^2 \to A[n]$.
an isomorhpism of ...
- 647
3
votes
0
answers
132
views
Arithmetic version of "Attaching maps" for moduli of curves
I am looking for a reference for attaching maps of moduli of curves with marked points. Especially I would like to know whether they descend over $\mathbb{Z}$. On one hand this seems very hard to ...
- 845
3
votes
0
answers
154
views
Examples of subspaces singled out by modular forms
I am wondering what subspaces of modular varieties defined as the zero locus of modular forms have been studied in the literature.
To be more clear let me explain the example I have in mind.
Let $N\...
- 231
2
votes
0
answers
171
views
A conjecture on the scheme-theoretic image of a moduli map
Let $K/\mathbb{Q}_p$ be a finite extension with residue field $k$, and let $K'/K$ be a finite tamely ramified Galois extension with residue field $k'$. Let $E/\mathbb{Q}_p$ be a sufficiently large ...
2
votes
0
answers
233
views
Representability of moduli problem of elliptic curves with complex multiplication
I'd like to know whether the moduli problem for elliptic curves with complex multiplication by a fixed imaginary quadratic number field $K$ (and with suitable level structure to be picked) is ...
- 91
1
vote
0
answers
278
views
Level structures in deformation spaces of $p$-divisible groups
I am reading (parts of) the paper "Moduli of $p$-divisible groups" by Scholze and Weinstein, and I am stuck at understanding the definition of level structures in Rapoport-Zink spaces (cf. Definition ...
- 83