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Published 2011 | public
Journal Article

Λ-adic modular symbols over totally real fields

Abstract

We consider a Hida family of nearly ordinary cusp forms on a quaternion algebra defined over a totally real number field. The aim of this work is to construct a cohomology class with coefficients in a p-adic sheaf over an Iwasawa algebra that can be specialized to cohomology classes attached to classical cusp forms in the given Hida family. Our result extends the work of Greenberg and Stevens on modular symbols attached to ordinary Hida families when the ground field is the field of rational numbers.

Additional Information

© 2011 Swiss Mathematical Society. Received December 20, 2007; revised April 2, 2009. This paper is part of the Ph.D thesis of the first author. The first author would like to sincerely thank his advisor Prof. F. Diamond for his help and encouragement. Both authors would like to thank Prof. H. Darmon for suggesting the problem and for his advice and support during their visits to McGill University. Finally, we sincerely thank the referee for his careful reading of the manuscript and for suggesting many valuable corrections and improvements.

Additional details

Created:
August 19, 2023
Modified:
October 24, 2023