Tag Archives: David Geraghty

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 Andrew Odlyzko, Chandrashekhar Khare, David Geraghty, David Renard, E_8, endoscopy, Gaëtan Chenevier, George Boxer, Harold Stark, Jack Thorne, James Newton, Jean Lannes, Jean-François Mestre, Jean-Marc Fontaine, Jean-Pierre Wintenberger, John Conway, Laurent Clozel, Leech Lattice, Michael Harris, Niemeier Lattices, Olivier Taîbi, Ramanujan's Delta, Stefane Fermigier, Stephen Miller, Toby Gee, Tom Barnet-Lamb | 6 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 10-author paper, Avner Ash, Barnett-Lamb, BLGGT, Chandrashekhar Khare, Dan Grayson, David Geraghty, Dwork, Gerd Faltings, Jean-Pierre Wintenberger, Lie Qian, Michael Harris, Nicholas Shepherd-Barron, Potential Automorphy, Richard Taylor, Serre, Toby Gee, Top, van Geemen | 1 Comment

Jacquet-Langlands and an old R=T conjecture

Posted on January 12, 2019 by Persiflage

This is part 2 of a series of posts on R=T conjectures for inner forms of GL(2). (See here for part 1). (Edit: this is still incorrect and there should have been a part 3, but I’ve been distracted… in … Continue reading →

Posted in Mathematics, Uncategorized | Tagged Akshay Venkatesh, blunders, Cohen-Macaulay, David Geraghty, Inner Forms, Jacquet-Langlands, Jeff Manning, Matthew Emerton, Multiplicities, Quaternion Algebras, R=T, Sherlock Holmes | 9 Comments

Abandonware

Posted on December 25, 2017 by Persiflage

For a young mathematician, there is a lot of pressure to publish (or perish). The role of for-profit academic publishing is to publish large amounts of crappy mathematics papers, make a lot of money, but at least in return grant … Continue reading →

Posted in Mathematics | Tagged Abandonware, Akshay Venkatesh, Andrew Odlyzko, Bernard Woolley, David Geraghty, Dick Gross, Discriminant Bounds, Galois Representations, Imaginary Quadratic Fields, Jacquet-Langlands, John Voight, Lassina Dembélé, Matthew Greenberg, Peter Sarnak, Publishing, Taylor-Wiles, Under The Cosh, Yes Minister | 4 Comments

Abelian Surfaces are Potentially Modular

Posted on November 11, 2017 by Persiflage

Today I wanted (in the spirit of this post) to report on some new work in progress with George Boxer, Toby Gee, and Vincent Pilloni. Edit: The paper is now available here. Recal that, for a smooth projective variety X … Continue reading →

Posted in Mathematics | Tagged Abelian Surfaces, Ana Caraiani, Andrew Wiles, Ariel Pacetti, Armand Brumer, Benoit Stroh, Betti cohomology, coherent cohomology, Cris Poor, David Geraghty, David Yuen, etale cohomology, George Boxer, Gonzalo Tornaría, Hasse-Weil Conjecture, Higher Hida Theory, IAS, Jacques Tilouine, John Voight, Kevin Buzzard, Kris Klosin, Langlands, Maass Forms, Payman Kassaei, Peter Scholze, RLT, Shekar Khare, Shepherd-Barron, Shu Susaki, Tetrachotomy, Tobias Berger, Toby Gee, Vincent Pilloni, Wintenberger, Yichao Tian | 12 Comments

New Results in Modularity, Part II

Posted on June 23, 2017 by Persiflage

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 Ana Caraiani, Andrew Wiles, Bao Le Hung, Barnett-Lamb, Barry Mazur, BLGGT, Breuil, Colmez, David Geraghty, David Helm, David Savitt, Diamond, Jack Thorne, James Newton, Ken Ribet, Laurent Clozel, Mark Kisin, Matthew Emerton, Michael Harris, Modularity, p-adic Langlands, Patrick Allen, Peter Scholze, RLT, Shekar Khare, Skinner, Taylor-Wiles, The Hawk, Toby Gee, Vytas Paskunas, Wintenberger | 7 Comments

New Results In Modularity, Part I

Posted on June 23, 2017 by Persiflage

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 | 13 Comments

A non-liftable weight one form modulo p^2

Posted on March 10, 2017 by Persiflage

I once idly asked RLT (around 2004ish) whether one could use Buzzard-Taylor arguments to prove that any representation: \(\rho: \mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q}) \rightarrow \mathrm{GL}_2(\mathbf{Z}/p^2 \mathbf{Z})\) which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). … Continue reading →

Posted in Mathematics | Tagged David Geraghty, RLT, Schaeffer, Weight one forms | Leave a comment

Artin No-Go Lemma

Posted on December 13, 2016 by Persiflage

The problem of constructing Galois representations associated to Maass forms with eigenvalue 1/4 is, by now, a fairly notorious problem. The only known strategy, first explained by Carayol, is to first transfer the representation to a unitary group over an … Continue reading →

Posted in Mathematics | Tagged Akshay Venkatesh, Artin Conjecture, Carayol, David Geraghty, Griffiths-Schmid Variety, l_0, Matthew Emerton, Notation | Leave a comment

Hilbert Modular Forms of Partial Weight One, Part III

Posted on October 17, 2015 by Persiflage

My student Richard Moy is graduating! Richard’s work has already appeared on this blog before, where we discussed his joint work with Joel Specter showing that there existed non-CM Hilbert modular forms of partial weight one. Today I want to … Continue reading →

Posted in Mathematics, Students | Tagged Andrei Jorza, David Geraghty, James Newton, Joel Specter, John Voight, Jordan Ellenberg, Lassina Dembélé, Martin Luu, Nathan Dunfield, Nigel Boston, Richard Moy | Leave a comment

Tag Archives: David Geraghty

Clozel 70, Part II

Potential Automorphy for GL(n)

Jacquet-Langlands and an old R=T conjecture

Abandonware

Abelian Surfaces are Potentially Modular

New Results in Modularity, Part II

New Results In Modularity, Part I

A non-liftable weight one form modulo p^2

Artin No-Go Lemma

Hilbert Modular Forms of Partial Weight One, Part III

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Tag Archives: David Geraghty

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