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Title: MOMENTS, MONODROMY, AND PERVERSITY. (AM-159)
A DIOPHANTINE PERSPECTIVE. (AM-159)
By: Nicholas M. Katz
Format: Paperback

List price: £118.00
Our price: £94.40
Discount:
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ISBN 10: 0691123306
ISBN 13: 9780691123301
Availability: Usually dispatched within 1-3 weeks.
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Publisher: PRINCETON UNIVERSITY PRESS
Pub. date: 12 September, 2005
Series: Annals of Mathematics Studies
Pages: 488
Description: 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.
Synopsis: 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.
Publication: US
Imprint: Princeton University Press
Returns: Returnable
Some other items by this author:
ARITHMETIC MODULI OF ELLIPTIC CURVES. (AM-108)
ARITHMETIC MODULI OF ELLIPTIC CURVES. (AM-108), VOLUME 108 (PB)
CONVOLUTION AND EQUIDISTRIBUTION
CONVOLUTION AND EQUIDISTRIBUTION (HB)
CONVOLUTION AND EQUIDISTRIBUTION (PB)
EXPONENTIAL SUMS AND DIFFERENTIAL EQUATIONS. (AM-124)
EXPONENTIAL SUMS AND DIFFERENTIAL EQUATIONS. (AM-124), VOLUME 124 (PB)
EXPONENTIAL SUMS, HYPERGEOMETRIC SHEAVES, AND MONODROMY GROUPS (HB)
EXPONENTIAL SUMS, HYPERGEOMETRIC SHEAVES, AND MONODROMY GROUPS (PB)
GAUSS SUMS, KLOOSTERMAN SUMS, AND MONODROMY GROUPS. (AM-116)
GAUSS SUMS, KLOOSTERMAN SUMS, AND MONODROMY GROUPS. (AM-116), VOLUME 116 (PB)
MOMENTS, MONODROMY AND PERVERSITY (HB)
MOMENTS, MONODROMY, AND PERVERSITY. (AM-159)
RANDOM MATRICES, FROBENIUS EIGENVALUES, AND MONODROMY
RANDOM MATRICES, FROBENIUS EIGENVALUES, AND MONODROMY (HB)
RIGID LOCAL SYSTEMS (HB)
RIGID LOCAL SYSTEMS. (AM-139)
RIGID LOCAL SYSTEMS. (AM-139), VOLUME 139 (PB)
THE GROTHENDIECK FESTSCHRIFT (PB)
THE GROTHENDIECK FESTSCHRIFT (PB)
THE GROTHENDIECK FESTSCHRIFT (PB)
TWISTED L-FUNCTIONS AND MONODROMY (HB)
TWISTED L-FUNCTIONS AND MONODROMY. (AM-150)
TWISTED L-FUNCTIONS AND MONODROMY. (AM-150), VOLUME 150 (PB)

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