Moments, Monodromy, and Perversityby Nicholas M. Katz
Moments, Monodromy, and Perversity: A Diophantine Perspective. (AM-159) (Annals of Mathematics Studies) by Nicholas M. Katz
Princeton University Press | October 2, 2005 | English | ISBN: 0691123306 | 481 pages | PDF | 1 MB
Princeton University Press | October 2, 2005 | English | ISBN: 0691123306 | 481 pages | PDF | 1 MB
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