Tag Archives: Barry Mazur

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

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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

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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

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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

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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

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Chenevier on the Eigencurve

Today I wanted to mention a theorem of Chenever about components of the Eigencurve. Let denote weight space (which is basically a union of discs), and let be the Coleman-Mazur eigencurve together with its natural map to It will do … Continue reading

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The decline and fall of Publications Mathématiques de l’lHÉS

I want to discuss the decline of a once great journal. How did IHES go from this: and this: to this: It is a sad state of affairs. To be clear, I am talking about the typesetting here. The old … Continue reading

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