ترغب بنشر مسار تعليمي؟ اضغط هنا

Geometric Satake, categorical traces, and arithmetic of Shimura varieties

90   0   0.0 ( 0 )
 نشر من قبل Xinwen Zhu
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English
 تأليف Xinwen Zhu




اسأل ChatGPT حول البحث

We survey some recent work on the geometric Satake of p-adic groups and its applications to some arithmetic problems of Shimura varieties. We reformulate a few constructions appeared in the previous works more conceptually.



قيم البحث

اقرأ أيضاً

168 - Thomas J. Haines 2013
We elaborate the theory of the stable Bernstein center of a $p$-adic group $G$, and apply it to state a general conjecture on test functions for Shimura varieties due to the author and R. Kottwitz. This conjecture provides a framework by which one mi ght pursue the Langlands-Kottwitz method in a very general situation: not necessarily PEL Shimura varieties with arbitrary level structure at $p$. We give a concrete reinterpretation of the test function conjecture in the context of parahoric level structure. We also use the stable Bernstein center to formulate some of the transfer conjectures (the fundamental lemmas) that would be needed if one attempts to use the test function conjecture to express the local Hasse-Weil zeta function of a Shimura variety in terms of automorphic $L$-functions.
276 - Yichao Tian , Liang Xiao 2013
Let $F$ be a totally real field in which $p$ is unramified. We study the Goren-Oort stratification of the special fibers of quaternionic Shimura varieties over a place above $p$. We show that each stratum is a $(mathbb{P}^1)^N$-bundle over other quat ernionic Shimura varieties (for some appropriate $N$).
74 - Qijun Yan 2021
Let $S$ be the special fibre of a Shimura variety of Hodge type, with good reduction at a place above $p$. We give an alternative construction of the zip period map for $S$, which is used to define the Ekedahl-Oort strata of $S$. The method employed is local, $p$-adic, and group-theoretic in nature.
86 - Xiaozong Wang 2020
Let $mathcal{X}$ be a regular projective arithmetic variety equipped with an ample hermitian line bundle $overline{mathcal{L}}$. We prove that the proportion of global sections $sigma$ with $leftlVert sigma rightrVert_{infty}<1$ of $overline{mathcal{ L}}^{otimes d}$ whose divisor does not have a singular point on the fiber $mathcal{X}_p$ over any prime $p<e^{varepsilon d}$ tends to $zeta_{mathcal{X}}(1+dim mathcal{X})^{-1}$ as $drightarrow infty$.
The integral model of a GU(n-1,1) Shimura variety carries a universal abelian scheme over it, and the dual top exterior power of its Lie algebra carries a natural hermitian metric. We express the arithmetic volume of this metrized line bundle, define d as an iterated self-intersection in the Gillet-Soule arithmetic Chow ring, in terms of logarithmic derivatives of Dirichlet L-functions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا