Let p be a prime number. Due to classical work of Shimura and Deligne, to any "newform" (a modular form that is an eigenfunction for the Hecke operators and assumed of level one in the talk) one attaches a padic Galois representation. Since there are infinitely many newforms, there are infinitely many attached padic Galois representations. However, if one reduces them modulo p, there are only finitely many (up to isomorphism). It is tempting to ask what happens "in between", i.e. whether there is still finiteness modulo fixed prime powers. In the talk, I will motivate and explain a conjecture made with Ian Kiming and Nadim Rustom and explain partial results, including a relation to a strong question by Kevin Buzzard. The talk is based on joint work with Ian Kiming and Nadim Rustom.
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Finiteness questions for Galois representations
Gabor Wiese
Institution:
Université du Luxembourg
Location:
Luigi Stasi Seminar Room, ICTP
Schedule:
Tuesday, January 29, 2019  15:30
Abstract:
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