## Moments, Monodromy, and Perversity: A Diophantine PerspectiveIt 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 |

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### Contents

II | 9 |

III | 12 |

IV | 13 |

VI | 21 |

VII | 24 |

VIII | 25 |

IX | 31 |

X | 36 |

LVII | 221 |

LVIII | 233 |

LIX | 240 |

LX | 245 |

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XI | 42 |

XII | 44 |

XIII | 45 |

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XV | 50 |

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XIX | 62 |

XXI | 64 |

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XXIII | 76 |

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XXVII | 96 |

XXIX | 97 |

XXX | 98 |

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XL | 138 |

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LXXX | 349 |

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LXXXVII | 409 |

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LXXXIX | 416 |

XC | 421 |

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XCII | 428 |

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C | 450 |

CI | 451 |

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Moments, Monodromy, and Perversity: A Diophantine Perspective Nicholas M. Katz No preview available - 2005 |