Companion forms and the structure of p-adic Hecke algebras
Number Theory
2007-05-23 v2
Abstract
We study the structure of the Eisenstein component of Hida's ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein ring if certain space of modular forms (mod p) having companions is one-dimensional; and also give a numerical criterion for this one-dimensionality. This in part overlaps with a work of Skinner and Wiles; but our method, based on a work of Ulmer, is totally different. We then consider consequences of the above mentioned Gorenstein property. We especially discuss the connection with the Iwasawa theory.
Cite
@article{arxiv.math/0403428,
title = {Companion forms and the structure of p-adic Hecke algebras},
author = {Masami Ohta},
journal= {arXiv preprint arXiv:math/0403428},
year = {2007}
}
Comments
29pages