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Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159)
Nicholas M. Katz
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Description for Moments, Monodromy, and Perversity. (AM-159): A Diophantine Perspective. (AM-159)
Paperback. Develops techniques based on two ingredients: the theory of perverse sheaves and Larsen's Alternative. These techniques are then used to calculate the geometric monodromy groups attached to some specific universal families of (L-functions attached to) character sums over finite fields. Series: Annals of Mathematics Studies. Num Pages: 488 pages, black & white illustrations. BIC Classification: PBH. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 254 x 178 x 16. Weight in Grams: 799.
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 ... Read more
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 ... Read more
Product Details
Format
Paperback
Publication date
2005
Publisher
Princeton University Press United States
Number of pages
488
Condition
New
Series
Annals of Mathematics Studies
Number of Pages
488
Place of Publication
New Jersey, United States
ISBN
9780691123301
SKU
V9780691123301
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1
About Nicholas M. Katz
Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of five previous books in this series: "Arithmetic Moduli of Elliptic Curves" (with Barry Mazur); "Gauss Sums, Kloosterman Sums, and Monodromy Groups"; "Exponential Sums and Differential Equations"; "Rigid Local Systems"; and "Twisted L-Functions and Monodromy".
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