Tag Archives: Mark Kisin

Unramified Fontaine-Mazur for representations coming from abelian varieties

Posted on May 9, 2024 by Persiflage

Mark Kisin gave a talk at the number theory seminar last week where the following problem arose: Let \(W\) be the Galois representation associated to the Tate module of an abelian variety \(A\) over a number field, and suppose that … Continue reading →

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The horizontal Breuil-Mezard conjecture

Posted on October 19, 2023 by Persiflage

Postdoc hiring season will be upon us soon! I have two excellent graduate students who will be applying for academic jobs soon, Chengyang Bao and Andreea Iorga. I have mentioned Chengyang’s first project before here and an introduction to the … Continue reading →

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En Passant VI

Posted on October 29, 2019 by Persiflage

I just learnt (from a comment on this blog) that Pierre Colmez hosts a wonderful page on Fontaine and Wintenberger here. I particularly recommend reading both the personal recollections of their friends and collaborators (sample quote from Mark: These \(p\)-adic … Continue reading →

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More or less OPAQUE

Posted on October 16, 2018 by Persiflage

I recently talked with Lynnelle Ye (a soon to be graduating student of Mark Kisin) for a few hours about her thesis and related mathematics. In her thesis, she generalizes (in part) the work Liu-Wan-Xiao on the boundary (halo) of … Continue reading →

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New Results in Modularity, Part II

Posted on June 23, 2017 by Persiflage

This is part two of series on work in progress with Patrick Allen, Ana Caraiani, Toby Gee, David Helm, Bao Le Hung, James Newton, Peter Scholze, Richard Taylor, and Jack Thorne. Click here for Part I It has been almost … Continue reading →

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Is Serre’s conjecture still open?

Posted on August 10, 2014 by Persiflage

The conjecture in this paper has indeed been proven. But that isn’t the entire story. Serre was fully aware of Katz modular forms of weight one. However, Serre was too timid was prudently conservative and made his conjecture only for … Continue reading →

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Local crystalline deformation rings

Posted on February 8, 2014 by Persiflage

I just returned from a very pleasant conference in Puerto Rico courtesy of the Simons Foundation (general advice: if you live in Chicago, always accept invitations to conferences in January). One thing I learnt from Toby Gee was the following … Continue reading →

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