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# Romyar Sharifi : A modular interpretation of a pairing on cyclotomic units

Class groups of cyclotomic fields have long been of central interest in number theory. We consider elements of these class groups that arise as values of a cup product pairing on cyclotomic units. These pairing values yield information on a wealth of algebraic objects, but any analytic interpretation of them was heretofore unknown. We will describe how, conjecturally, modular representations can be used to relate the pairing values to p-adic L-values of cusp forms.

**Category**: Algebraic Geometry**Duration**: 01:34:44**Date**: April 16, 2008 at 4:25 PM**Views**: 177-
**Tags:**seminar, Algebraic Geometry Seminar

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