Learning seminar on p-adic geometry (Spring 2023)

We will study p-adic geometry and its applications to the local Langlands correspondence, roughly following the Berkeley lectures.

Primary references

R. Huber, Continuous valuations
R. Huber, A generalization of formal schemes and rigid analytic varieties
R. Huber, Étale cohomology of rigid analytic varieties and adic spaces
P. Scholze, Étale cohomology of diamonds
T. Wedhorn, The local Langlands correspondence for GL(n) over p-adic fields
T. Wedhorn, Adic Spaces
Geometrization of the Local Langlands program (Montreal conference notes by Tony Feng)
Geometrization of the Local Langlands correspondence (lectures by Laurent Fargues, notes by Sean Howe)

Date	Speaker	Topic	References
Feb 10	Dan	Adic spaces	[SW] 2, [W1] 1.1-1.5
Feb 17	Zheng	Adic spaces	[SW] 2.3, 3, [W1] 1.6-1.8
Feb 24	John	Adic spaces	[SW] 4, 5.2, [W1] 1.9
Mar 3	Jacksyn	Perfectoid rings	[SW] 6
Mar 24	Alice	Perfectoid spaces	[SW] 7, [W1] 2.4
Mar 31	Zecheng	Diamonds	[SW] 8, 9.4, [W1] 3.2-3.4
Apr 7^*	Meng	Diamonds	[SW] 10, [W1] 3.4-3.5
Apr 14	Jacksyn	Local Langlands	[W2] 1, 2.1-2.2, [SW] I
Apr 21	Vijay	Fargues-Fontaine curve	[SW] 11.2-11.3, 13.5, [W1] 2.5, 4.2, [FS] I.3, [W2] 2.4, 3.2-3.3, [K] 3
Apr 28	Jared	Stacks, Bun_G	[V], [Sta] 072H, [FS] I.2, I.4
May 5	Dan	Geometrization of local Langlands	[FS] I

^* Time and location change: 3:30pm in Harvard Science Center 112