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# Romyar Sharifi : Modular symbols and arithmetic

I will explain how to attach ideal classes of cyclotomic fields to geodesics in the complex upper half-plane. A conjecture of mine states this construction is inverse to another arising from the Galois action on cohomology of modular curves modulo an Eisenstein ideal. I hope to use this to motivate a broader philosophy, developed jointly with Takako Fukaya and Kazuya Kato, that certain arithmetic objects attached to Galois representations of global fields can be described using higher-dimensional modular symbols.

**Category**: Number Theory**Duration**: 01:34:46**Date**: April 6, 2016 at 1:25 PM**Views**: 110-
**Tags:**seminar, Number Theory Seminar

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