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 |