Geometry and Cohomology of Some Simple Shimura Varieties
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...
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...
