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Thursday, February 22, 2018

**Abstract:** In the 1990s, Kolyvagin and Rubin introduced the Euler system of Gauss sums to derive upper bounds on the sizes of the p-primary parts of the ideal class groups of certain cyclotomic ﬁelds. Since then, this and other Euler systems have been studied in order to analyze other number-theoretic structures. Recent work has shown that Kolyvagin’s Euler system appears naturally in the context of various conjectures by Gross, Rubin, and Stark involving special values of L-functions. We will discuss these Euler systems from this new point of view as well as a related result about the module structure of various ideal class groups over Iwasawa algebras.