清华主页 EN
导航菜单

The plectic conjecture over local fields

来源: 09-22

时间:10:00-11:00 Beijing time, Sep 27, 2022

地点:Zoom ID: 293 812 9202 Passcode: BIMSA Room: BIMSA 1118

主讲人:Siyan Daniel Li-Huerta

Abstract:

The étale cohomology of varieties over Q enjoys a Galois action. For Hilbert modular varieties, Nekovář-Scholl observed that this Galois action on the level of cohomology extends to a much larger profinite group: the plectic group. Motivated by applications to higher-rank Euler systems, they conjectured that this extension holds even on the level of complexes, as well as for more general Shimura varieties.

We present a proof of the analog of this conjecture for local Shimura varieties. Consequently, we obtain results for the basic locus of global Shimura varieties, after restricting to a decomposition group. The proof crucially uses a mixed-characteristic version of fusion due to Fargues–Scholze.


返回顶部
相关文章
  • Dowling-Wilson conjecture and equivariant compactification of the vector group

    Abstract:In the first part of the talk, I will give a survey of the proof of the Dowling-Wilson conjecture using the Schubert variety of a hyperplane arrangement. The Schubert variety of a hyperplane arrangement is an equivariant compactification of the vector group with finitely many orbits. In the second part of the talk, we will discuss a recent work of Colin Crowley characterizing Schubert...

  • Zagier's Polylogarithm Conjecture revisited

    AbstractInstigated by work of Borel and Bloch, Zagier formulated his Polylogarithm Conjecture in the late eighties and proved it for weight 2. After a flurry of activity and advances at the time, notably by Goncharov who provided not only a proof for weight 3 but set out a vast program with a plethora of conjectural statements for attacking it, progress seemed to be stalled for a number of year...