Galois representations, automorphic forms, and the Sato-Tate Conjecture

Michael Harris ()
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Michael Harris: Université Paris 7

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 5, 707-746

Abstract: Abstract The present text consists of notes of several lectures on the proof of the Sato-Tate Conjecture given up through 2008. The goal of the lectures was to explain the statement and the main ideas of the proof. The notes are somewhat dated; shortly after they were written, the author, together with Bernet-Lamb, Geraghty, and Taylor, were able to prove the analogue of the Sato-Tate conjecture for all elliptic modular forms. In particular, Theorems 2.4 and 2.5 are not conditional, and the condition on the j-invariant in Theorem 1.1 is superfluous. Moreover, the methods of proof outlined in sections 3 and 4 have been generalized and extended in a number of ways, notably in a series of articles by Barnet-Lamb, Gee, Geraghty, and Taylor, by Thorne, and by Calegari and Geraghty.

Keywords: Elliptic curve; Sato-Tate Conjecture; automorphic representation; Galois representation; Taylor-Wiles method (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0085-4

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