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Category Archives: Mathematics
A nonliftable weight one form modulo p^2
I once idly asked RLT (around 2004ish) whether one could use BuzzardTaylor arguments to prove that any representation: which was unramified at p and residually irreducible (and modular) was itself modular (in the Katz sense). Galois representations of this flavour … Continue reading
Complain about MSRI day
I will be heading off later this week to the Academic Sponsors’ Day at MSRI, going as Shmuel’s proxy for uchicago. I’m not sure to what extent (if any) there is for me to make policy suggestions, but any comments … Continue reading
Posted in Mathematics, Politics
Tagged Kevin Buzzard, MSRI, SatoTate, Shmuel, University of Chicago, wag
14 Comments
Virtual coherent cohomology
I gave a talk yesterday where I attempted to draw parallels between the cohomology of (arithmetic) 3manifolds and weight one modular forms. It was natural then to think about whether there was an analogue of the virtual Betti number conjecture. … Continue reading
Posted in Mathematics
Tagged Ian Agol, Melbourne, Mumford, Shimura Curves, Spin Structures, Virtual Positive Betti Number
6 Comments
The class number 100 problem
Some time ago, Mark Watkins busted open the “class number n” problem for smallish n, finding all imaginary quadratic fields of class number at most 100 (the original paper is here) Although the paper describes the method in detail, it … Continue reading
Posted in Mathematics, Uncategorized
Tagged 1842523, 5519, 97, Arithmetic Groups, Class Number Problem, Ellenberg, Gauss, Helfgott, Hyperbolic 3manifolds, LMFDB, Mark Watkins, MO, Pierce, Venkatesh
8 Comments
Central Extensions, Updated
I previously mentioned a problem concerning polynomials, whose motivation came from thinking about weight one forms and the inverse Galois problem for finite subgroups of I still like the polynomial problem, but I realized that I was confused about the … Continue reading
Posted in Mathematics
Tagged A5, Darstellungsgruppe, Inverse Galois Problem, Trivialities
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Correspondance SerreTate, Part I
Reading the correspondence between Serre and Tate has been as delightful as one could expect. What is very nice to see — although perhaps not so surprising — is the utter delight that both Serre and Tate find in discussing … Continue reading
Posted in Mathematics
Tagged 118982593, 144169, 3457, 691, 97, Deuring, minus part, Mumford, Odlyzko, plus part, Rene Schoof, Serre, SerreTate Correspondence, Tate, Tate Conjecture
4 Comments
Artin NoGo Lemma
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, GriffithsSchmidt Variety, l_0, Matthew Emerton, Notation
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