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Meta
Tag Archives: Stefan Patrikis
SL_n versus GL_n
I recently wrote a paper (with Toby Gee and George Boxer, see also here) on constructing regular algebraic automorphic representations \(\pi\) of (cohomological) weight zero and level one, and therefore also cuspidal cohomology classes in the cohomology of \(\mathrm{GL}_n(\mathbf{Z})\) for … Continue reading
Posted in Mathematics
Tagged AI, ChatGPT, Gaëtan Chenevier, George Boxer, Go, Grunwald-Wang Theorem, Hilbert modular forms, Jack Thorne, James Newton, Jean-Pierre Labesse, Joachim Schwermer, John Tate, Jürgen Rohlfs, Karen Vogtmann, la langue française, Laurent Clozel, Nasit Darshan, Pierre Colmez, Raghuram, Serre, Serre-Tate Correspondence, Stefan Patrikis, Tate, Toby Gee
1 Comment
Potential Modularity of K3 surfaces
This post is to report on results of my student Chao Gu who is graduating this (academic) year. If \(A/F\) is an abelian surface, then one can associate to \(A\) a K3 surface \(X\) (the Kummer surface) by blowing up … Continue reading
Posted in Mathematics, Work of my students
Tagged Chao Gu, George Boxer, Morrison, Picard Group, Picard Rank, Stefan Patrikis, Tate Conjecture, Toby Gee, Vincent Pilloni
2 Comments
Polymath Proposal: 4-folds of Mumford’s type
Let \(A/K\) be an abelian variety of dimension \(g\) over a number field. If \(g \not\equiv 0 \bmod 4\) and \(\mathrm{End}(A/\mathbf{C}) = \mathbf{Z}\), then Serre proved that the Galois representations associated to \(A\) have open image in \(\mathrm{GSp}_{2g}(\mathbf{Z}_p)\). The result … Continue reading
Irregular Lifts, Part I
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
Inverse Galois Problems II
David Zywina was in town today to talk about a follow up to his previous results mentioned previously on this blog. This time, he talked about his construction of Galois groups which were simple of orthogonal type, in particular, the … Continue reading