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Reciprocity maps and Selmer groups

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If you have a question about this talk, please contact Mustapha Amrani.

Non-Abelian Fundamental Groups in Arithmetic Geometry

This talk concerns certain homomorphisms that arise in the study of Galois cohomology with restricted ramification. Given a set S of primes of a number field containing all those above a given prime p, the S-reciprocity map is a homomorphism on S-units that interpolates values of a cup product with those S-units. We will discuss the properties of and connections between this and related homomorphisms, and study their application to Selmer groups of reducible representations. Finally, we will explore a connection with a conjecture of the author on the relationship between these maps for cyclotomic fields and a modular two-variable p-adic L-function, taken modulo an Eisenstein ideal.

This talk is part of the Isaac Newton Institute Seminar Series series.

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