Math 206 - Topics in Algebraic Geometry (UCSD and online, spring 2021)

Course description: The topic for this course is prismatic cohomology. This is a form of p-adic cohomology, similar in nature to crystalline cohomology or rigid cohomology, introduced by Bhatt and Scholze in the late 2010s. It has several advantages, including having fairly simple foundations; giving rise to a concise derivation of integral p-adic Hodge theory; and exhibiting some very suggestive links with q-de Rham cohomology that point toward a future theory of "arithmetic crystalline cohomology".

Due to the COVID-19 pandemic and UCSD campus regulations, this course will be offered online (except for some in-person office hours). Lectures will be given remotely via Zoom, with Zoom links posted to Canvas and Zulip. Announcements will be made via Zulip (see below).

Online epicourse: I plan to follow the model of my pandemic-era courses Math 204A and Math 204B and stage a parallel "epicourse" consisting of the following components. (All times are local to San Diego, which is UTC-7 throughout this course.)

Use this Google Form to join the epicourse.

Note that the lecture recordings and lecture notes will be posted publicly here, so you do not need to join the epicourse to get those. However, I hope the other interactions via Zoom and Zulip will add significant value, and encourage everyone following the lectures to join.

Environment: In both the course and the epicourse, I aim to create a conducive learning environment for those who do not see themselves reflected in the mathematical profession at present or have experienced systemic bias affecting their mathematical education. I insist that all participants do their part to maintain this environment. I also aim to address accessibility issues as best I can; please let me know directly if this might affect you.

Instructor: Kiran Kedlaya, kedlaya [at] ucsd [etcetera].

Lectures: MWF 2-2:50pm. I will try to post each recording within 30 minutes of the completion of the lecture.

Office hours: Timings may be adjusted during the term.

Textbook: None; I will post lecture notes in HTML and PDF formats (generated by PreTeXt; see my GitHub repository). These notes will be based on some combination of the following:

Prerequisites: Math 203A-C or permission of instructor. While prismatic cohomology is closely linked with the theory of perfectoid spaces, no prior knowledge of that topic will be assumed.

Homework: None.

Final exam: None. Disregard any information from the UCSD Registrar to the contrary.

Grading: Let me know if you need a meaningful grade for this course, in which case I will propose some sort of final writing project.

Key dates:

Topics by date (with videos, references, and boards): See also this page for the videos embedded as iframes, or this playlist for all the videos together.