| 5/30 (Mon) | 5/31 (Tue) | 6/1 (Wed) | 6/2 (Thu) | 6/3 (Fri) | |
|---|---|---|---|---|---|
| 9:00--10:15 | Görtz | Caraiani | Liu | Shen | Chen |
| 10:45--12:00 | Mieda | Hsieh | Madapusi Pera | Hattori | Hamacher |
| 12:00--14:00 | Lunch Break | ||||
| 14:00--15:15 | Nie | Kim | Free | Boxer | Zhou |
| 15:45--17:00 | Yu | Smithling | Free | Zhang | Shin |
Reception: 5/30 (Mon) after the last talk
Banquet: 6/2 (Thu) 18:00
Speaker: George Boxer, University of Chicago
Title: Coherent cohomology of Shimura varieties and derived Hecke algebras
Abstract:
James Newton and Jack Thorne have defined "derived Hecke algebras" which act on the cohomology of arithmetic locally symmetric spaces at the derived category level. They use the work of Scholze to show that in suitable situations there are Galois representations valued in these derived Hecke algebras. This was motivated by the work of Calegari and Geraghty on extending the Taylor-Wiles method to this setting. In my talk I will describe an analogous story for the coherent cohomology of automorphic vector bundles on Shimura varieties, and I will describe how this may be applied to the locally symmetric space setting via a construction of boundary cohomology.
Speaker: Ana Caraiani, Princeton University and Institute for Advanced Study
Title: On the generic part of cohomology of compact unitary Shimura varieties
Abstract:
I will discuss joint work with Peter Scholze showing that torsion in the cohomology of certain compact unitary Shimura varieties occurs in the middle degree, under a genericity assumption on the corresponding Galois representation.
Speaker: Miaofen Chen, East China Normal University
Title: A decomposition of affine Deligne-Lusztig varieties
Abstract:
We propose a new stratification of the reduced subschemes of the moduli spaces of p-divisible groups and of affine Deligne-Lusztig varieties for the unramified groups which generalizes stratifications for special cases such as the Bruhat-Tits stratification of Vollaard and Wedhorn, and the semi-module stratification of de Jong and Oort. And we will discuss its basic properties. (Joint work with Eva Viehmann)
Speaker: Ulrich Görtz, Universität Duisburg-Essen
Title: Basic Loci of EKOR type
Abstract:
As is known from the work of, among others, Vollaard-Wedhorn, Rapoport-Terstiege-Wilson, Howard-Pappas, in certain cases the basic locus of a Shimura variety admits a simple description as a union of classical Deligne-Lusztig varieties, where the index set of the union (and the closure relations of strata) have a description in terms of a Bruhat-Tits building.
We describe a group-theoretic approach to this phenomenon, based on an analysis of the corresponding affine Deligne-Lusztig varieties. The talk is based on joint work with Xuhua He, and work in progress with Xuhua He and Sian Nie.
Speaker: Paul Hamacher, Technische Universität München
Title: The geometry of the Newton strata in Shimura varieties of Hodge type
Abstract:
I construct a generalisation of Mantovan's almost product structure to Shimura varieties of Hodge type with hyperspecial level structure at p to show that the perfection of the Newton strata are pro-étale locally isomorphic to the perfection of the product of a central leaf and a Rapoport-Zink space. In particular I derive the dimension formula and closure relations of the Newton strata. The almost product formula can be extended to obtain an analogue of Caraiani's and Scholze's generalisation of the almost product structure for Shimura varieties of Hodge type.
Speaker: Shin Hattori, Kyushu University
Title: On a properness of the Hilbert eigenvariety at integral weights
Abstract:
Let p be a rational prime. It is known that for various reductive algebraic groups G over Q, Hecke eigensystems of p-adic overconvergent automorphic forms of finite slopes on G are parametrized by a rigid analytic variety, called eigenvariety. Eigenvarieties have been subjects of many interesting researches, while their geometry is not well-understood. One of the cases where much progress has been made is the eigenvariety for GL_2---the Coleman-Mazur eigencurve. For example, its properness over the weight space, which is an analog of the classical notion of properness in algebraic geometry, is proved by Diao-Liu.
On the other hand, the theory of canonical subgroups of abelian varieties is useful not only to construct some eigenvarieties but also to study how overconvergent modular forms are analytically continued over PEL Shimura varieties. In this talk, I will explain how to show the properness of Andreatta-Iovita-Pilloni's eigenvariety of Hilbert cuspidal eigenforms at integral weights for some cases, using the theory of canonical subgroups.
Speaker: Ming-Lun Hsieh, National Taiwan University
Title: Hida families and p-adic L-functions for triple products
Abstract:
In this talk, we will give a construction of the p-adic L-functions attached to three Hida families of elliptic newforms and show the explicit interpolation formula at all critical specialisations in the balanced range. The derivatives of this p-adic L-function at exceptional zero points will also be discussed.
Speaker: Wansu Kim, King's College London
Title: RZ Spaces of Hodge type
Abstract:
In this talk, we review the definition and construction of Rapoport-Zink spaces of Hodge type (in the unramified case), together with various natural properties generalizing the (P)EL case. (One small addition is the action of a certain perfectoid group of self quasi-isogenies on Hodge-type Rapoport-Zink spaces, as in the work of Caraiani and Scholze.) And then we discuss the possibility of extending the construction to tamely ramified cases, granting some natural conjecture.
Speaker: Ruochuan Liu, BICMR, Peking University
Title: Rigidity of p-adic local systems and application to Shimura varieties
Abstract:
I will report some recent progress on de Rham rigidity of p-adic local systems as well as its application to Shimura varieties.
Speaker: Yoichi Mieda, University of Tokyo
Title: Cohomology of affinoids in the Lubin-Tate space at infinite level and their reductions
Abstract:
Under some conditions, I will compare the l-adic cohomology of an affinoid in the Lubin-Tate space at infinite level and that of the reduction of its formal model. I will also give some applications on the local Langlands correspondence.
Speaker: Keerthi Madapusi Pera, University of Chicago
Title: On the average height of abelian varieties with complex multiplication
Abstract:
In the 90s, generalizing the classical Chowla-Selberg formula, P. Colmez formulated a conjectural formula for the Faltings heights of abelian varieties with multiplication by the ring of integers in a CM field, which expresses them in terms of logarithmic derivatives at 1 of certain Artin L-functions. Using ideas of Gross, he also proved his conjecture for abelian CM extensions. In this talk, I will explain a proof of Colmez's conjecture in the average for an arbitrary CM field. This is joint work with F. Andreatta, E. Goren and B. Howard.
Speaker: Sien Nie, Chinese Academy of Sciences
Title: On the density of the ordinary locus
Abstract:
An interesting question on reductions of Shimura varieties is: when are the ordinary loci dense? Positive answers are obtained for certain cases by several people. Based on several axioms formulated by He and Rapoport, we give a classification of the quasi-split cases (with parahoric level structures) where the basic loci are dense. This is a joint work with He.
Speaker: Xu Shen, Chinese Academy of Sciences
Title: Local and global geometric structures of perfectoid Shimura varieties
Abstract:
In this talk, we will investigate some geometric structural properties of perfectoid Shimura varieties of abelian type. In the global part, we will construct some minimal and toroidal type compactifications for these spaces, and we will describe explicitly the degeneration of Hodge-Tate period map at the boundaries. In the local part, we will show that each Newton stratum of these perfectoid Shimura varieties can be described by the related (generalized) Rapoport-Zink space and Igusa variety. As a consequence of our local and global constructions, we can compute the stalks of the relative cohomology under the Hodge-Tate period map of the intersection complex (on the minimal compactification), in terms of cohomology of Igusa varieties at the boundary with truncated coefficients.
Speaker: Sug Woo Shin, University of California, Berkeley
Title: Patching and p-adic Langlands for GL(2,Q_p)
Abstract:
I will present joint work with Caraiani, Emerton, Gee, Geraghty, and Paskunas on a new construction of the p-adic local Langlands correspondence for GL(2,Q_p) via our patching construction based on the Taylor-Wiles and Kisin method. The correspondence in this case has been previously established by Colmez and further analyzed by Colmez, Dospinescu, and Paskunas. Our construction is independent of theirs, recovers several (but not all) properties of the correspondence, and might shed some light on various related problems such as the local-global compatibility.
Speaker: Brian Smithling, Johns Hopkins University
Title: Arithmetic transfer conjectures for unitary groups
Abstract:
The arithmetic fundamental lemma is a conjectural relation proposed by W. Zhang in connection with a relative trace formula approach to the hermitian case of the arithmetic Gan-Gross-Prasad conjecture. It asserts a deep relation between the derivative of an orbital integral and an intersection number for cycles in a formal moduli space of p-divisible groups attached to an unramified unitary group over a p-adic field. I will report on some joint work with M. Rapoport and W. Zhang towards enlarging the scope of the conjecture to cases where ramification is allowed in various ways; in such cases the conjecture is recast as the so-called arithmetic transfer conjecture. The key feature in these cases is that relevant formal moduli spaces are regular.
Speaker: Chia-Fu Yu, Academia Sinica
Title: On Non-emptiness of Newton strata of Shimura varieties
Abstract:
We will discuss a class of integral models of Shimura varieties equipped with a notion of Newton stratification. These models can be constructed by taking the closure and normalization. We then show non-emptiness of the basic locus provided the integral model satisfies an admissible condition, and non-emptiness of Newton strata provided in addition the defining group G is quasi-split at p. We will also discuss non-emptiness of Ekedahl-Oort strata and Kottwitz-Rapoport strata.
Speaker: Chao Zhang, YMSC, Tsinghua University
Title: Level m stratifications on Shimura varieties of Hodge type
Abstract:
In this talk, I will explain some geometric properties of level m stratifications on good reductions of Shimura varieties of Hodge type. The method is to construct certain torsors as well as equivariant morphisms which are closely related to truncated displays. If there is still time, I will also explain some applications to Newton strata.
Speaker: Rong Zhou, Harvard University
Title: Mod-p points on Shimura varieties with parahoric level structure
Abstract:
The Langlands-Rapoport conjecture gives a conjectural description of the Fp-points of a suitable integral model of a Shimura variety. Results of this kind are useful, for example, in computing the local factor of the semi-simple zeta function of the Shimura variety. We prove a version of this conjecture for certain cases of Hodge type Shimura varieties with parahoric level constructed by Kisin and Pappas.