Number theory learning seminar 2014-2015

In the winter and spring the seminar will meet Mondays 2:30--4:30pm in Room 384I on the first week of winter, and 384H in subsequent weeks. This year's seminar will focus on the perfectoid spaces. In the fall we will discuss adic spaces (and their relation with rigid-analytic geometry), in the winter we will discuss the basics of perfectoid spaces (especially the tilting functor and the almost purity theorem), and in the spring we will discuss some applications to p-adic Hodge theory.

For more details on what each lecture will cover with references see here .

Here are some references which may be relevant for this year's seminar:
(BV) Stably uniform affinoids are sheafy, by Buzzard-Verberkmoes
(F) Perfectoides, presque purete et monodromie-poids, by Fontaine
(GR) Almost ring theory, Springer LNM 1800, by Gabber--Ramero
(H0) Bewertungsspektrum und rigide Geometrie, by Huber
(H1) Continuous valuations, by Huber
(H2) A generalization of formal schemes and rigid-analytic varieties, by Huber
(H3) Etale cohomology of rigid-analytic varieties and adic spaces, by Huber
(P) Maximally complete fields, by Poonen
(S1) Perfectoid spaces, by Scholze
(S2) Perfectoid spaces: a survey, by Scholze
(S3) p-adic Hodge theory for rigid-analytic varieties, by Scholze
(W) Adic spaces, by Wedhorn (unpublished notes)



Notes -- use at your own risk.

These are informal notes. They may change without warning.

Fall quarter
1 Sept. 26 Conrad Motivation for adic spaces .pdf
2 Oct. 3 Conrad Spaces of valuations .pdf
3 Oct. 10 Conrad Spectral spaces and constructible sets .pdf
4 Oct. 17 Conrad Specialization constructions .pdf
5 Oct. 24 Conrad Huber rings and continuous valuations .pdf
6 Oct. 31 Conrad More constructions with Huber rings .pdf
7 Nov. 7 Conrad Rational domains, Tate rings, and analytic points. .pdf
8 Nov. 14 Conrad More properties for Cont(A) .pdf
9 Nov. 21 Conrad Spectrality of Cont(A) .pdf
10 Dec. 5 Conrad Affinoid adic spaces I .pdf
11 Dec. 12 Conrad Affinoid adic spaces II .pdf
Winter quarter
12 Jan. 5 Conrad Structure presheaves and rational domains .pdf
13 Jan. 12 Evan Uniformity and sheaf properties .pdf
14 Jan. 19 Conrad Basic generalities on adic spaces .pdf
15 Jan. 26 Conrad Points and lft morphisms .pdf
16 Feb. 2 Conrad Rigid geometry and perfectoid rings .pdf
17 Feb. 9 Conrad The tilting functor .pdf
Spring quarter
18 April 8-May 11 Masullo Foundations of perfectoid geometry, I (being edited)
19 May 18-June 1 Masullo Foundations of perfectoid geometry, II