BUNTES: p-adic Hodge Theory

2024 Spring


Spring 2024 BUNTES will cover foundations and topics in p-adic Hodge Theory (pHT). Meetings will occur in-person at Boston University's CDS building.

The first half of the semester will be dedicated to the motivation, formulation, and constructions in the foundations of pHT. This includes the notions of Hodge-Tate representations, formalisms of admissible representations, and the various period rings along with their additional structures. We will largely follow the first two parts of Brinon and Conrad's notes linked below.

The remainder of the semester will be dedicated to the study of p-divisible groups. The goal is to use the foundation of p-adic Hodge Theory we've established in the first half of the seminar and read Tate's seminal paper within this language.

The main references for the first half will be Brinon and Conrad's notes [BrCo], though speakers may elect to lean on one of the plethora of other specialized notes available online. The main references for the second half will be Tate's original paper [Tate] and Benois's Introduction to p-adic Hodge Theory [Ben].


Meeting Times: Thursdays 2:30 PM - 3:30 PM
Location: CDS 524


Date Topic Speaker Reference
Jan 25 Motivation and Hodge-Tate Representations John BrCo Sec 1,2
Feb 1 Etale phi-modules and Examples Kate BrCo Sec 3
Feb 8 Formalism of Admissible Representations and Examples Jacksyn BrCo Sec 5
Feb 15 de Rham Period Ring and de Rham Representations James BrCo Sec 4,6
Feb 22 Filtered Isocrystals Xinyu BrCo Sec 7
Feb 29 Crystalline Representations Zecheng :)
Mar 28 Semistable Representations Zecheng .-.
Apr 4 Formal Groups and Duality Jacksyn Tate Sec 2.1 - 2.3
Apr 11 Galois Modules and Examples Kate Tate Sec 2.4
Apr 18 Totally Ramified Extensions Xinyu Tate Sec 3.1, 3.2
Apr 25 Hodge-Tate Decomposition James Tate Sec 4.1, Ben Sec 14
May 2 Main Theorem and p-adic HT John Tate Sec 4.2, Ben Sec 14