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.
Read Online or Download The Geometry and Cohomology of Some Simple Shimura Varieties. PDF
Similar Algebraic Geometry books
The 1st biography of Oscar Zariski - arguably one of many maximum mathematicians of the twentieth century. established principally on interviews with Zariski, his family members, and his colleagues, it features a precis of a few of his pioneering paintings in addition to his own heritage which spans approximately eighty years and covers many of the globe.
The invention of recent algorithms for facing polynomial equations, and their implementation on quickly, reasonably cheap desktops, has revolutionized algebraic geometry and resulted in interesting new purposes within the box. This publication info many makes use of of algebraic geometry and highlights contemporary functions of Grobner bases and resultants.
Quantity 2: Schemes and intricate Manifolds, covers generalizations in diversified instructions of the affine and projective forms that shape the fabric for the 1st quantity. Discusses the origins of algebraic geometry. Paper. DLC: Geometry - Algebraic.
Extra info for The Geometry and Cohomology of Some Simple Shimura Varieties.