Vol. 9, No. 1, 2015

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Eisenstein Hecke algebras and conjectures in Iwasawa theory

Preston Wake

Vol. 9 (2015), No. 1, 53–75
Abstract

We formulate a weak Gorenstein property for the Eisenstein component of the p-adic Hecke algebra associated to modular forms. We show that this weak Gorenstein property holds if and only if a weak form of Sharifi’s conjecture and a weak form of Greenberg’s conjecture hold.

Keywords
Iwasawa theory, Hecke algebra, Gorenstein, Eisenstein, Sharifi's conjecture, Greenberg conjecture
Mathematical Subject Classification 2010
Primary: 11R23
Secondary: 11F33
Milestones
Received: 16 January 2014
Revised: 13 October 2014
Accepted: 6 December 2014
Published: 18 February 2015
Authors
Preston Wake
Department of Mathematics
University of Chicago
Eckhart Hall
Chicago, IL 60637
United States