Tag Archives: Chandrashekhar Khare

Clozel 70, Part II

Posted on September 30, 2023 by Persiflage

Many years ago, Khare asked me (as I think he asked many others at the time) whether I believed their existed an irreducible motive \(M\) over \(\mathbf{Z}\) (so good reduction everywhere) with Hodge-Tate weights \([0,1,2,\ldots,n-1]\) for any \(n > 1\). … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , , , , , , , , | 5 Comments

30 years of modularity: number theory since the proof of Fermat

Posted on July 8, 2022 by Persiflage

It’s probably fair to say that the target audience for this blog is close to orthogonal to the target audience for my talk, but just in case anyone wants to watch it in HD (and with the audio synced to … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 13 Comments

Potential Automorphy for GL(n)

Posted on April 29, 2021 by Persiflage

Fresh on the arXiv, a nice new paper by Lie Qian proving potential automorphy results for ordinary Galois representations \(\rho: G_F \rightarrow \mathrm{GL}_n(\mathbf{Q}_p)\) of regular weight \([0,1,\ldots,n-1]\) for arbitrary CM fields \(F\). The key step in light of the 10-author … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , , , , , , , , , , , | 1 Comment

Irregular Lifts, Part I

Posted on October 19, 2018 by Persiflage

This post motivated in part by the recent preprint of Fakhruddin, Khare, and Patrikis, and also by Matt’s number theory seminar at Chicago this week. (If you are interested in knowing what the calendar is for the Chicago number theory … Continue reading →

Posted in Mathematics | Tagged , , , , , , , , | 7 Comments