Tag Archives: Barry Mazur

Schaefer and Stubley on Class Groups

I talked previously about work of Wake and Wang-Erickson 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

Posted in Mathematics | Tagged , , , , , , , , , | Leave a comment

Mathieu Magic

I previously mentioned that I once made (in a footnote) the false claim that for a 11-dimensional 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 , , , , , , | 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 , , , , , , , , , , , , , , , , , , , , , , , , , , , , | 6 Comments

Pseudo-representations 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

Posted in Mathematics | Tagged , , , , , , , , , | 4 Comments

Z_p-extensions 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 , , , , , , | Leave a comment

Z_p-extensions 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 , , , | 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 , , , , , , | 7 Comments