Michael Harris, Richard Taylor, "The Geometry and Cohomology of Some Simple Shimura Varieties."
English | 2001 | ISBN: 0691090920, 0691090904 | PDF | pages: 279 | 16.0 mb
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "simple" Shimura varieties. These two problems go hand in hand. The results represent a major advance in algebraic number theory, finally proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of local class field theory.
