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Tag Archives: Barry Mazur
Schaefer and Stubley on Class Groups
I talked previously about work of Wake and WangErickson on deformations of Eisenstein residual representations. In that post, I also mentioned a paper of Emmanuel Lecouturier who has also proved some very interesting theorems. Today, I wanted to talk about … Continue reading →
Mathieu Magic
I previously mentioned that I once made (in a footnote) the false claim that for a 11dimensional representation V of the Mathieu group M_12, the 120 dimensional representation Ad^0(V) was irreducible. I had wanted to write down representations W of … Continue reading →
Posted in Mathematics

Tagged Barry Mazur, Emmanuel Kowalski, Liubomir Chirac, Magaard, Malle, Mathieu Group, Tiep

3 Comments
New Results in Modularity, Part II
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 →
Posted in Mathematics

Tagged Ana Caraiani, Andrew Wiles, Bao Le Hung, BarnettLamb, Barry Mazur, BLGGT, Breuil, Colmez, David Geraghty, David Helm, Diamond, Jack Thorne, James Newton, Ken Ribet, Laurent Clozel, Mark Kisin, Matthew Emerton, Michael Harris, Modularity, padic Langlands, Patrick Allen, Peter Scholze, RLT, Shekar Khare, Skinner, TaylorWiles, Toby Gee, Vytas Paskunas, Wintenberger

6 Comments
Pseudorepresentations and the Eisenstein Ideal
Preston Wake is in town, and on Tuesday he gave a talk on his recent joint work with Carl Wang Erickson. Many years ago, Matt and I studied Mazur’s Eisenstein Ideal paper from the perspective of Galois deformation rings. Using … Continue reading →
Z_pextensions of Number Fields, Part II
This is continuation of the last post. We claimed there that we were going to deform a totally real number field of degree n into a field with signature (r,s) with r+2s = n, and pass information about Leopoldt’s conjecture … Continue reading →
Posted in Mathematics

Tagged Ankeny, Barry Mazur, Brauer, Chowla, Deformations, Leopoldt Conjecture, Yuri Bilu

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Z_pextensions of Number Fields, Part I
In the next few posts, I want to discuss a problem that came up when I wrote a paper with Barry Mazur. We had a few observations and remarks that we discussed as part of a possible sequel but which … Continue reading →
Posted in Mathematics

Tagged Barry Mazur, Deforming Number Fields, Leopoldt Conjecture, Serpentine

1 Comment
Tensor Products
Let be an irreducible representation of a finite group Say that is tensor indecomposable if any isomorphism implies that either or is a character. In conversations with Matt and Toby (which permeate the rest of this post as well), the … Continue reading →
Posted in Mathematics

Tagged Barry Mazur, Indecomposable Representations, Mathieu Group, Matthew Emerton, Representation Theory, Simple Groups, Toby Gee

7 Comments