This volume deals with the properties of cohomology of Siegel varieties with coefficients in \(\mathbb Z_p\) or in a certain local system of flat \(\mathbb Z_p\)-modules. The main result of the book establishes the absence of \(p\)-torsion in certain localizations of this cohomology. Two arithmetic applications are presented: One concerns Hida families of Hecke eigensystems, and the other is a step towards the existence of certain Taylor-Wiles systems for symplectic groups.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Readership

Graduate students and research mathematicians interested in algebraic geometry and group representations.

Table of Contents

• A. Mokrane and J. Tilouine -- Cohomology of Siegel varieties with \(p\)-adic integral coefficients and applications
• P. Polo and J. Tilouine -- Bernstein-Gelfand-Gelfand complexes and cohomology of nilpotent groups over \(\mathbb{Z}_{(p)}\) for representations with \(p\)-small weights