The Geometry and Cohomology of Some Simple Shimura Varieties. (Am-151), Volume 151
by Michael Harris and Richard Taylor


Overview -

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.  Read more...


 
In Stock.

This item is Non-Returnable.
FREE Shipping for Club Members
 
> Check In-Store Availability

In-Store pricing may vary

 
 
New & Used Marketplace 10 copies from $75.22
 
eBook
Retail Price: $99.95
$72.11

Add to Cart + Add to Wishlist

Download

This item is available only to U.S. and Canada billing addresses.
 
 
 

More About The Geometry and Cohomology of Some Simple Shimura Varieties. (Am-151), Volume 151 by Michael Harris; Richard Taylor
 
 
 
Overview

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, asserts the existence of a correspondence, with certain formal properties, relating n-dimensional representations of the Galois group of K with the representation theory of the locally compact group GLn(K). This book constructs a candidate for such a local Langlands correspondence on the vanishing cycles attached to the bad reduction over the integer ring of K of a certain family of Shimura varieties. And it proves that this is roughly compatible with the global Galois correspondence realized on the cohomology of the same Shimura varieties. The local Langlands conjecture is obtained as a corollary.


Certain techniques developed in this book should extend to more general Shimura varieties, providing new instances of the local Langlands conjecture. Moreover, the geometry of the special fibers is strictly analogous to that of Shimura curves and can be expected to have applications to a variety of questions in number theory.



This item is Non-Returnable.

 
Details
  • ISBN-13: 9780691090924
  • ISBN-10: 0691090920
  • Publisher: Princeton University Press
  • Publish Date: November 2001
  • Page Count: 288
  • Dimensions: 9.18 x 6.12 x 0.7 inches
  • Shipping Weight: 0.91 pounds

Series: Annals of Mathematics Studies (Paperback) #144

Related Categories

Books > Mathematics > Number Theory
Books > Mathematics > Geometry - Algebraic

 
BAM Customer Reviews