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Tag Archives: Andrew Wiles
Update on SatoTate for abelian surfaces
Various people have asked me for an update on the status of the SatoTate conjecture for abelian surfaces in light of recent advances in modularity lifting theorems. My student Noah Taylor has exactly been undertaking this task, and this post … Continue reading
Posted in Mathematics
Tagged Ana Caraiani, Andrew Sutherland, Andrew Wiles, Bao Le Hung, Christian Johansson, David Helm, Francesc Fité, Freydoon Shahidi, George Boxer, Henry Kim, Jack Thorne, James Newton, Kiran Kedlaya, Laurent Clozel, Michael Harris, Nick Katz, Noah Taylor, Patrick Allen, Peter Scholze, Potential Modularity, Richard Taylor, SatoTate, Serre, Toby Gee, Victor Rotger, Vincent Pilloni
2 Comments
New Results In Modularity, Part I
I usually refrain from talking directly about my papers, and this reticence stems from wishing to avoid any appearance of tooting my own horn. On the other hand, nobody else seems to be talking about them either. Moreover, I have … Continue reading
Posted in Mathematics
Tagged Ana Caraiani, Andrew Wiles, Bao Le Hung, Blasius, David Geraghty, David Helm, Deligne, Don Blasius, Functoriality, Gowers, Jack Thorne, James Newton, Langlands, Laurent Clozel, Michael Harris, Modularity, Nuno Freitas, Patrick Allen, Peter Scholze, Port, Ramanujan, Reciprocity, RLT, Samir Siksek, Serre, The Triangle, Toby Gee
12 Comments
There are no unramified abelian extensions of Q (almost)
In my class on modularity, I decided to explain what Wiles’ argument (in the minimal case) would look like for . There are two ways one can go with this. On the one hand, one can try to prove (say) … Continue reading