BUNTES: p-adic Hodge Theory

2024 Spring

Overview

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 either integral pHT, the formalism of phi-Gamma modules, or almost mathematics. The decision will be made later depending on the organizer and participants' interest.

The main references 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.

Announcements

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

Schedule

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 TBD
Mar 21 Semistable Representations TBD TBD
TBD More to come ... TBD TBD