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Finiteness questions for Galois representations
Wiese, Gabor
2019
 

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Abstract :
[en] 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 p-adic Galois representation. Since there are infinitely many newforms, there are infinitely many attached p-adic 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.
Disciplines :
Mathematics
Author, co-author :
Wiese, Gabor  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Finiteness questions for Galois representations
Publication date :
29 January 2019
Event name :
Mathematics Seminar at International Center for Theoretical Physics
Event place :
Trieste, Italy
Event date :
29 January 2019
Audience :
International
Available on ORBilu :
since 20 December 2019

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