Hecke algebras associated to $Λ$-adic modular forms

Mathematics – Number Theory

Scientific paper

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13 pages

Scientific paper

We show that if an Eisenstein component of the $p$-adic Hecke algebra
associated to modular forms is Gorenstein, then it is necessary that the
plus-part of a certain ideal class group is trivial. We also show that this
condition is sufficient whenever a conjecture of Sharifi holds.

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