Seminar

Speaker: Heejong Lee (Purdue University)

Date: July 4 (Thus) 4pm & July 5 (Fri) 4pm

Venue: Bldg 108 Rm 319

 

1. 첫번째 강연(7월5일 오후 4시):  Geometry of irreducible components inside the Emerton-Gee stack, I

2. 두번째 강연(7월6일 오후 4시): Geometry of irreducible components inside the Emerton-Gee stack, II

 

Abstract: The Emerton-Gee stack provides a geometric framework to study p-adic Galois representations and their families. It plays a central role in recent progress on the Serre weight conjectures and the formulation of the categorical mod p and p-adic local Langlands conjecture.

One of the most striking features of the Emerton-Gee stack is that irreducible components in its reduced substack bijects with irreducible representations of the finite group GL_n(F_q) with mod p coefficients. Here, we already see a connection between Galois representations and representations of (finite) reductive groups, as we anticipate in the Langlands program.

In the first talk, I will introduce the Emerton-Gee stack while providing some relevant backgrounds(e.g.algebraic stacks). Then I will discuss what is known about its irreducible components(with illustration).

In the second talk, I will discuss a work in progress studying the geometry of irreducible components.