Math 711, Fall 2012.
Topics in Algebra
The local Langlands correspondence
My office is 4859 East Hall,
and my office hours are Wednesdays, 1:10-2pm and Thursdays, 1-4pm.
The class meets on Mondays, Wednesdays and Fridays, 12pm-1pm,
in room 4096 of East Hall.
Optional homework in PDF (last updated: 11/05/2012)
There will be three main themes in the course:
- Geometric construction of representations of finite and
p-adic reductive groups
- Formal groups and their applications (not only to the
local Langlands program)
- Various approaches to geometry over totally
disconnected fields (such as Q_p),
including (as time permits) rigid analytic, adic and perfectoid spaces.
Approximate course contents (arranged by
week)
- Principal series representations of GL_2 over a finite
field (week of September
5,7).
- Cuspidal representations of GL_2 over a finite field;
introduction to smooth representations of p-adic groups (week of
September 10).
- Principal series representations of GL_2 over a p-adic
field (week of
September 17).
- More on principal series for GL_2(F); some odds and
ends (week of September 24).
- Hecke algebras and supercuspidal representations (week
of October 1).
- Examples of supercuspidal representations of GL_n(F);
general comments on the local Langlands correspondence (week of October
8).
- Representations of Weil groups of local fields (October
17). No class on October 19.
- Introduction
to formal groups (week of October 22).
- Formal groups over fields of characteristic p>0 (week
of October
29).
- Formal modules and Lubin-Tate theory (week of November
5).
- Deformation spaces of formal modules (week of November
12).
- Introduction to rigid analytic spaces (week of November
19).
- Definition and examples of rigid analytic spaces (week
of November 26).
- Rigid generic fibers of formal schemes; the Lubin-Tate
tower (week of December 3).
- The local Langlands and Jacquet-Langlands
correspondences (week of December 10).