A universal Galois representation attached to modular forms modulo 2

作者：Bellaiche Joel^*

来源：Comptes Rendus Mathematique, 2012, 350(9-10): 443-448.

DOI：10.1016/j.crma.2012.04.012

Let A be the algebra of Hecke operators acting on mod 2 cusp forms of level 1 and any weight. Nicolas and Serre have determined the structure of A: one has A similar or equal to F-2[[x, y]]. Let G(Q,2) be the Galois group of the maximal extension of Q unramified outside 2 and infinity, and let G be its maximal pro-2-quotient. One constructs a continuous Galois representation r: G -%26gt; SL2(A) such that tr r(Frob(p)) = T-p for all odd prime p. One also proves its uniqueness and one studies its irreducibility properties.

• 出版日期2012-5