Algebraic Geometry

Download E-books Rigid Local Systems. (AM-139) PDF

By Nicholas M. Katz

Riemann brought the concept that of a "local approach" on P1-{a finite set of issues} approximately one hundred forty years in the past. His concept used to be to review nth order linear differential equations through learning the rank n neighborhood structures (of neighborhood holomorphic options) to which they gave upward thrust. His first program used to be to review the classical Gauss hypergeometric functionality, which he did through learning rank-two neighborhood structures on P1- {0,1,infinity}. His research was once profitable, principally simply because this kind of (irreducible) neighborhood method is inflexible within the experience that it's globally made up our minds once one understands individually every one of its neighborhood monodromies. It turned transparent that good fortune performed a task in Riemann's good fortune: so much neighborhood platforms aren't inflexible. but many classical features are ideas of differential equations whose neighborhood structures are inflexible, together with either one of the traditional nth order generalizations of the hypergeometric functionality, n F n-1's, and the Pochhammer hypergeometric functions.

This booklet is dedicated to developing all (irreducible) inflexible neighborhood structures on P1-{a finite set of issues} and spotting which collections of independently given neighborhood monodromies come up because the neighborhood monodromies of irreducible inflexible neighborhood systems.

Although the issues addressed the following return to Riemann, and appear to be difficulties in advanced research, their suggestions count primarily on loads of very fresh mathematics algebraic geometry, together with Grothendieck's etale cohomology thought, Deligne's facts of his far-reaching generalization of the unique Weil Conjectures, the idea of perverse sheaves, and Laumon's paintings at the l-adic Fourier Transform.

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