Papers

For more recent papers I am now linking straight to ArXiv. This saves me from having to update the timestamp on this web page. I fix typos in my papers and upload the new versions to ArXiv, so that's always the best place to look for my papers. To search for all my ArXiv papers at once, try clicking here.

"A computation of modular forms of weight one and small level", with Alan Lauder. ArXiv. DOI: 10.1007/s40316-016-0072-8. To appear in Annales mathématiques du Québec.

"Slopes of modular forms", with Toby Gee. ArXiv or here's a slightly better pdf (13th April 2016) which doesn't have the bad line breaks, and where we have fixed two non-serious typos ("the first numbers" -> "the numbers" at top of p6, and heading of table on p6). DOI 10.1007/978-3-319-41424-9_2. Pages 93--109 of Families of automorphic forms and the trace formula, Ed. Mueller, Shin, Templier.

"Stably uniform affinoids are sheafy", with Alain Verberkmoes. ArXiv. To appear in Crelle (DOI 10.1515/crelle-2015-0089).

"Playing simple loony dots and boxes endgames optimally", with Michael Ciere. ArXiv. Integers 14 (2014), Paper No. G08.

"Computing weight 1 modular forms over C and F_p-bar". ArXiv. In "Computations With Modular Forms 2011" (edited by G. Boeckle, G. Wiese), Contributions in Mathematical and Computational Sciences, Springer, 2014.

"Explicit reduction modulo $p$ of certain 2-dimensional crystalline Galois representations, II", with Toby Gee. ArXiv. Bull. London Math. Soc. (2013) 45 (4): pages 779--788 (current ArXiv version is April 2016 -- ArXiv version has fixed the typos in the statements of Lemma 3.2(1) and Cor 4.7(1) ).

"Potential modularity---a survey". Pages 188--211 of "Non-abelian fundamental groups and Iwasawa theory", London Mathematical Society Lecture Note Series, 393. Edited by John Coates, Minhyong Kim, Florian Pop, Mohamed Saidi and Peter Schneider. dvi or pdf. Last modified April 2011.

"The conjectural connections between automorphic representations and Galois representations", with Toby Gee. dvi or pdf. Last modified Aug 2015 (fixing an issue with Hodge-Tate weights spotted by Florian Herzig). Appeared in the conference proceedings for the LMS/EPSRC Durham Symposium "Automorphic Forms and Galois Representations (2011)".

"On Serre's conjecture for mod ell Galois representations over totally real fields", with Fred Diamond and Frazer Jarvis, Duke Math Journal Vol 55 no. 1, 2010, pp105--161, dvi or pdf. Last modified April 2010.

"Explicit reduction modulo p of certain crystalline representations", with Toby Gee, IMRN 2009, no. 12, 2303--2317. dvi or pdf. Last modified Feb 2009.

"Eigenvarieties", in "$L$-functions and Galois representations", 59--120, London Math. Soc. Lecture Note Ser., 320, Cambridge Univ. Press, Cambridge, 2007. dvi or pdf (last updated 02/08/06).

"The 2-adic eigencurve is proper", with F. Calegari, dvi or pdf, Documenta Mathematica 2006, Extra Vol., 211--232 (last updated 05/07/05). That version assumes some standard facts about the 2-adic eigencurve. A slightly longer version of the paper, containing proofs of these facts, is here: dvi or pdf (also last updated 05/07/05).

"The 2-adic eigencurve at the boundary of weight space", with L. Kilford, Compositio Math. 141 (2005), 605--619, dvi or pdf, (last updated 04/06/04).

"Slopes of overconvergent 2-adic modular forms", with F. Calegari, Compositio Math. 141 (2005), 591--604, dvi or pdf,

"A counterexample to the Gouvea-Mazur conjecture", with F. Calegari, Comptes rendus - Mathematiques, Vol 338/10 (2004), pp 751--753, dvi or pdf, (last updated 28 Aug 03).

"On p-adic families of automorphic forms", pp23--44 of "Modular Curves and Abelian Varieties", Progress in Maths 224, Birkhauser, dvi or pdf (last updated 12 Oct 2004).

"Questions about slopes of modular forms", pp1--15 of "Formes Automorphes (I)", Asterisque 298, dvi or pdf. Computer programs related to this paper are here.

"Analytic continuation of overconvergent eigenforms", Journal of the American Math. Society 16 (2003), pp29--55. dvi or pdf

"A mod 5 approach to the modularity of icosahedral Galois representations", with W. Stein, Pacific Journal of Mathematics Vol 203 No 2 (2002), pp265-282, dvi or pdf.

"On icosahedral Artin representations", with M. Dickinson, N. Shepherd-Barron and R. Taylor, Duke Math Journal Vol 109 No 2 (2001), pp283-318, dvi or pdf.

"Families of modular forms", Journal de Th\'eorie des Nombres de Bordeaux, Vol 13 Fasc. 1 (2001), pp43--52, dvi or pdf.

"A mod l multiplicity one result", appendix to "Lectures on Serre's Conjectures" by K. Ribet and W. Stein, Arithmetic Algebraic Geometry, B. Conrad and K. Rubin, eds., IAS/Park City Mathematics Series vol. 9, AMS, dvi or pdf.

"On level lowering for mod 2 representations", Mathematical Research Letters 7, pp95--110 (2000), dvi or pdf.

"Companion forms and weight 1 forms" (with Richard Taylor), Annals of Maths Vol.149 (1999), 905--919, dvi or pdf.

"Integral models of certain Shimura curves", Duke Math Journal, Vol.87,No.3, 1997, dvi or pdf.

"On the eigenvalues of the Hecke operator T_2", Journal of Number Theory, Vol 57 No.1, March 1996, dvi or pdf.

Kevin Buzzard is buzzard at ic.ac.uk