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.
The local Langlands conjecture for GLn(K), where K is a p-adic field,...
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 deco...
