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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2005, Issue 585


Companion forms and the structure of p-adic Hecke algebras

Masami Ohta
Published Online: 2005-11-07 | DOI: https://doi.org/10.1515/crll.2005.2005.585.141


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.

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Published Online: 2005-11-07

Published in Print: 2005-08-26

Citation Information: Journal für die reine und angewandte Mathematik, Volume 2005, Issue 585, Pages 141–172, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crll.2005.2005.585.141.

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