This volume is the first of a series of two devoted to automorphic forms from a geometric and arithmetic point of view. They also deal with certain parts of the Langlands program. The themes treated in this volume include $p$-adic modular forms, the local Langlands correspondence for $GL(n)$, the cohomology of Shimura varieties, their reduction modulo $p$, and their stratification by Newton polygons.

The book is suitable for graduate students and research mathematicians interested in number theory, algebra, and algebraic geometry.

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 number theory, algebra, and algebraic geometry.

Table of Contents

• K. Buzzard -- Questions about slopes of modular forms
• M. Harris -- The local Langlands correspondence: Notes of $($half$)$ a course at the $IHP$ Spring 2000
• H. Hida -- $p$-adic automorphic forms on reductive groups
• F. Oort -- Newton polygons and $p$-divisible groups: a conjecture by Grothendieck
• M. Rapoport -- A guide to the reduction modulo $p$ of Shimura varieties
• L. Saper -- $\mathcal L$-modules and the conjecture of Rapoport and Goresky-MacPherson
• D. Soudry -- On Langlands functoriality from classical groups to $\mathrm{GL}_n$
• M. Strauch -- On the Jacquet-Langlands correspondence in the cohomology of the Lubin-Tate deformation tower