| Talk_id | Date | Speaker | Title |
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29417
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Monday 9/26
3:00 PM
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Patrick Daniels, University of Michigan
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Canonical integral models for Shimura varieties defined by tori
- Patrick Daniels, University of Michigan
- Canonical integral models for Shimura varieties defined by tori
- 09/26/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Georgios Pappas (pappasg@msu.edu)
Pappas and Rapoport have recently conjectured the existence of canonical integral models for Shimura varieties with parahoric level structure, which are characterized using Scholze's theory of p-adic shtukas. We will illustrate the conjecture using the example of Shimura varieties defined by tori, where (surprisingly) the theory is already nontrivial. Along the way we will explain a connection with the Bhatt-Scholze theory of prismatic F-crystals.
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29445
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Monday 10/10
3:00 PM
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Pavel Čoupek, MSU
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Ramification bounds for mod p étale cohomology via prismatic cohomology
- Pavel Čoupek, MSU
- Ramification bounds for mod p étale cohomology via prismatic cohomology
- 10/10/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Preston Wake (wakepres@msu.edu)
Let $K/\bf{Q}_p$ be a local number field of absolute ramification index $e$, and let $X$ be a proper smooth $O_K$-scheme. I will discuss how one can obtain bounds on ramification of the mod $p$ Galois representations arising as the étale cohomology of (the geometric generic fiber of) $X$ in terms of $e$, the given prime $p>2$ and the cohomological degree $i$. The key tools for achieving this are the Breuil-Kisin and $A_{\rm inf}$-cohomology theories of Bhatt, Morrow and Scholze, and a series of conditions based on a criterion of Gee and Liu regarding crystallinity of the representation attached to a free Breuil-Kisin-Fargues $G_K$-module.
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30469
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Monday 10/17
3:00 PM
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Preston Wake, MSU
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Rational torsion in modular Jacobians
- Preston Wake, MSU
- Rational torsion in modular Jacobians
- 10/17/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Preston Wake (wakepres@msu.edu)
I will talk about Ogg's conjecture and its generalization. This is joint work with Ken Ribet (and should serve as an introduction to Ken's talk on Friday).
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29434
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Friday 10/21
3:00 PM
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Ken Ribet, UC Berkeley
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Cyclotomic torsion points on abelian varieties over number fields
- Ken Ribet, UC Berkeley
- Cyclotomic torsion points on abelian varieties over number fields
- 10/21/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Preston Wake (wakepres@msu.edu)
Over 40 years ago, I proved the finiteness of the group of cyclotomic torsion points on an abelian variety over a number field. (A torsion point is cyclotomic if its coordinates lie in the field obtained by
adjoining all roots of unity to the base field.) If the abelian variety is one that we know well, and if the number field is the field of rational numbers, we can hope to determine explicitly the group of
its cyclotomic torsion points. I will illustrate this theme in the situation studied by Barry Mazur in his landmark "Eisenstein ideal" article, i.e., that where the abelian variety is the Jacobian of the
modular curve $X_0(p)$.
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29396
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Monday 10/24
3:00 PM
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Nathan Chen, Columbia University
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On the irrationality of some algebraic varieties and their subvarieties
- Nathan Chen, Columbia University
- On the irrationality of some algebraic varieties and their subvarieties
- 10/24/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Laure Flapan (flapanla@msu.edu)
The classical question of determining which varieties are rational has led to a huge amount of interest and activity. On the other hand, one can take on a complementary perspective - given a smooth projective variety whose nonrationality is known, how far is it from being rational? I will survey what is currently known, with an emphasis on hypersurfaces and complete intersections.
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29443
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Monday 10/31
3:00 PM
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Stephanie Chan, UMich
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Integral points in families of elliptic curves
- Stephanie Chan, UMich
- Integral points in families of elliptic curves
- 10/31/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Preston Wake (wakepres@msu.edu)
Given an elliptic curve over a number field with its Weierstrass model, we can study the integral points on the curve. Taking an infinite family of elliptic curves and imposing some ordering, we may ask how often a curve has an integral point and how many integral points there are on average. We expect that elliptic curves with any non-trivial integral points are generally very sparse. In certain quadratic and cubic twist families, we prove that almost all curves contain no nontrivial integral points.
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29399
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Monday 11/7
3:00 PM
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Qingjing Chen, University of California Santa Barbara
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Kuznetsov components of some Fano fourfolds
- Qingjing Chen, University of California Santa Barbara
- Kuznetsov components of some Fano fourfolds
- 11/07/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Laure Flapan (flapanla@msu.edu)
Kuznetsov component A_X of an algebraic variety X is defined to be the right orthogonal of some exceptional collection in the bounded derived category of X. When X is a cubic fourfold or Gushel Mukai fourfold, A_X is a noncommutative K3 surface in the sense that its Serre functor is given by "shifting by 2". Whether or not A_X is equivalent to the bounded derived category of an actual K3 surface is believed to be related to the rationality of the variety X , therefore it has received extensive studies. Yet not many studies seem to answer the question of when the Kuznetsov component of a cubic fourfold is equivalent to that of a Gushel Mukai fourfold, we believe that the answer of this question should be interesting for it will give a part of "Torelli theorem for noncommutative K3 surfaces". In this talk, I will present some partial results which address the previous question.
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29394
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Monday 11/14
3:00 PM
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Lena Ji, University of Michigan
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Finite order birational automorphisms of Fano hypersurfaces
- Lena Ji, University of Michigan
- Finite order birational automorphisms of Fano hypersurfaces
- 11/14/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Joseph Waldron (waldro51@msu.edu)
The birational automorphism group is a natural birational invariant associated to an algebraic variety. In this talk, we study the specialization homomorphism for the birational automorphism group. As an application, building on work of Kollár and of Chen–Stapleton, we show that a very general n-dimensional complex hypersurface X of degree ≥ 5⌈(n+3)/6⌉ has no finite order birational automorphisms. This work is joint with Nathan Chen and David Stapleton.
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30449
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Monday 11/28
3:00 PM
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Zijian Yao, University of Chicago
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The eigencurve over the boundary of the weight space
- Zijian Yao, University of Chicago
- The eigencurve over the boundary of the weight space
- 11/28/2022
- 3:00 PM - 4:00 PM
- C304 Wells Hall
- Preston Wake (wakepres@msu.edu)
The eigencurve is a rigid analytic curve that $p$-adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious. However, over the boundary, it is predicted to behave rather nicely (by the so-called Halo conjecture). This conjecture has been studied by Liu--Wan--Xiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of $\rm{GL}(2)$. If time permits, we will discuss some generalizations towards groups beyond $\rm{GL}(2)$. This is partially joint with H. Diao.
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