ZhengTong Chern-Weil Symposium Spring 2025: Jacob Tsimerman (UToronto)
Автор: University of Chicago Department of Mathematics
Загружено: 2025-05-28
Просмотров: 331
Diophantine Results for Shimura Varieties
Abstract:
Shimura Varieties are higher dimensional analogues of modular curves, and they play a foundational role in modern number theory. The most familiar Shimura varieties are the moduli spaces of Abelian varieties, and in this context we have a wealth of diophantine results, both in the number field and function field setting: Finiteness of S-rational points, the Tate conjecture, the Shafarevich conjecture, semisimplicity of Galois representations, and others. We focus on the exceptional setting for Shimura varieties, where the lack of a moduli interpretation makes matters more difficult. We explain some analogues of the aforementioned results. Crucial to this is the construction of canonical integral models, which we do at almost all primes. This is joint work with Ben Bakker and Ananth Shankar.
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