Reference : Finiteness questions for Galois representations
Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/41370
Finiteness questions for Galois representations
English
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
29-Jan-2019
International
Mathematics Seminar at International Center for Theoretical Physics
29 January 2019
Trieste
Italy
[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.
http://hdl.handle.net/10993/41370

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