Moments, monodromy, and perversity a diophantine perspective
Moments, monodromy, and perversity: a diophantine perspective

It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions...

Full description

Saved in:
Bibliographic Details
Main Author: Katz, Nicholas M. 1943- (Author)
Format: Electronic eBook
Language:English
Published: Princeton, NJ Princeton University Press [2005]
Series:Annals of Mathematics Studies number 159
Subjects:
L-functions
Monodromy groups
Sheaf theory
Monodromiegruppe
Garbentheorie
L-Funktion
Online Access:DE-1046
DE-859
DE-860
DE-739
DE-1043
DE-858
Volltext
Summary:It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family obeys a "generalized Sato-Tate law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family. Up to now, nearly all techniques for determining geometric monodromy groups have relied, at least in part, on local information. In Moments, Monodromy, and Perversity, Nicholas Katz develops new techniques, which are resolutely global in nature. They are based on two vital ingredients, neither of which existed at the time of Deligne's original work on the subject. The first is the theory of perverse sheaves, pioneered by Goresky and MacPherson in the topological setting and then brilliantly transposed to algebraic geometry by Beilinson, Bernstein, Deligne, and Gabber. The second is Larsen's Alternative, which very nearly characterizes classical groups by their fourth moments. These new techniques, which are of great interest in their own right, are first developed and then used to calculate the geometric monodromy groups attached to some quite specific universal families of (L-functions attached to) character sums over finite fields
Item Description:Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016)
Physical Description:1 online resource
ISBN:9781400826957
DOI:10.1515/9781400826957

There is no print copy available.

Interlibrary loan Place Request Caution: Not in THWS collection! Get full text

Similar Items