Mathematics – Number Theory
Scientific paper
2012-02-16
Mathematics
Number Theory
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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