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Galois Seminar

Friday, February 23, 2018 - 3:15pm

Romyar Sharifi



University of Pennsylvania


I will describe what may seem a strange relationship between two maps that occur in the cohomology of number fields.  This comparison, together with a conjecture of mine, can be used to study the structure of Selmer groups of twists of ordinary Eisenstein components of the first cohomology groups of modular curves.  The latter étale cohomology groups have quotients that are canonical lattices in the Galois representations attached to newforms congruent to Eisenstein series.  This relates to earlier work of Greenberg and Vatsal: we study the opposite parity.