Level-raising and symmetric power fuctoriality, II

Laurent Clozel (1) , Jack A. Thorne (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 HARVARD - Department of Mathematics [Cambridge]

A simple instance of the conjectured Lannglands functoriality is the existence of the symmetric powers Sym^n of a cuspidal representation of GL(2) over the adeles of a number field F . In this paper, the second of a series, we prove the existence of S^5 and S^7 when F is totally real (verifying a simple condition) and the representation of GL(2) comes from classical modular forms of weight at least 2. The proofs rely on new advances in the Taylor-Wiles deformation theory of Galois representations.

Mots clés: Langlands L-functions; Galois representations

Domaines: Théorie des nombres [math.NT]

Laurent Clozel, Jack A. Thorne. Level-raising and symmetric power fuctoriality, II. 2014. ⟨hal-01026329⟩