Eisenstein Hecke algebras and conjectures in Iwasawa theory

Preston Wake

doi:10.2140/ant.2015.9.53

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Home > Journals > Algebra Number Theory > Volume 9 > Issue 1 > Article

2015 Eisenstein Hecke algebras and conjectures in Iwasawa theory

Preston Wake

Algebra Number Theory 9(1): 53-75 (2015). DOI: 10.2140/ant.2015.9.53

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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.

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Preston Wake. "Eisenstein Hecke algebras and conjectures in Iwasawa theory." Algebra Number Theory 9 (1) 53 - 75, 2015. https://doi.org/10.2140/ant.2015.9.53