Download E-books The Geometry and Cohomology of Some Simple Shimura Varieties. PDF

By Michael Harris

This ebook goals first to turn out the neighborhood Langlands conjecture for GLn over a p-adic box and, moment, to spot the motion of the decomposition staff at a first-rate of undesirable relief at the l-adic cohomology of the "simple" Shimura forms. those difficulties pass hand in hand. the implications characterize a huge strengthen in algebraic quantity conception, eventually proving the conjecture first proposed in Langlands's 1969 Washington lecture as a non-abelian generalization of neighborhood type box theory.

The neighborhood Langlands conjecture for GLn(K), the place okay is a p-adic box, asserts the lifestyles of a correspondence, with definite formal homes, pertaining to n-dimensional representations of the Galois team of K with the illustration conception of the in the neighborhood compact team GLn(K). This publication constructs a candidate for one of these neighborhood Langlands correspondence at the vanishing cycles connected to the undesirable relief over the integer ring of K of a undeniable kin of Shimura forms. And it proves that this is often approximately appropriate with the worldwide Galois correspondence discovered at the cohomology of a similar Shimura kinds. The neighborhood Langlands conjecture is got as a corollary.

Certain ideas constructed during this publication may still expand to extra common Shimura forms, supplying new cases of the neighborhood Langlands conjecture. additionally, the geometry of the targeted fibers is precisely analogous to that of Shimura curves and will be anticipated to have functions to numerous questions in quantity theory.

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