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Companion forms and the structure of p-adic Hecke algebras
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Masami Ohta
Published/Copyright:
November 7, 2005
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.
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Published Online: 2005-11-07
Published in Print: 2005-08-26
Walter de Gruyter GmbH & Co. KG
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Articles in the same Issue
- Sur certaines identités endoscopiques entre transformées de Fourier
- Canonical heights, transfinite diameters, and polynomial dynamics
- Severi varieties and their varieties of reductions
- Companion forms and the structure of p-adic Hecke algebras
- An explicit matching theorem for level zero discrete series of unit groups of p-adic simple algebras
Articles in the same Issue
- Sur certaines identités endoscopiques entre transformées de Fourier
- Canonical heights, transfinite diameters, and polynomial dynamics
- Severi varieties and their varieties of reductions
- Companion forms and the structure of p-adic Hecke algebras
- An explicit matching theorem for level zero discrete series of unit groups of p-adic simple algebras
