## Galois groups and their representations: proceedings of a Symposium held in Nagoya from December 14, 1981 until December 18, 1981 |

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### Contents

Tomio Kubota Notes on Metaplectic Automorphic Functions | 1 |

Takayuki Oda Hodge Structures of Shimura Varieties Attached | 15 |

Masami Ohta On the Zeta Function of an Abelian Scheme | 37 |

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### Common terms and phrases

abelian scheme abelian varieties algebraic group algebraic number field algebraically closed assume canonical isomorphism Chapter I Section class field theory closure Cm(X cohomology complete discrete valuation conjecture connected etale contained corresponding curve of genus definition denotes dimensional local fields discrete valuation field divisor exact sequence exists field of fractions finite extension finite field Frobenius function field Galois extension Galois group Hasse-Witt invariants Hecke operators Hence Hilbert modular Hn(Mf Hodge structure homomorphism idele class group induced integer invertible irreducible isomorphism Kq(k Lemma Let F maximal modular form modulus morphism n-ordinary natural number normal subgroup obtain open subscheme phism prime ideal prime number Proposition prove quaternion algebra quotient representation residue field residue homomorphism resp respect ring satisfying Shimura curves Spec surjective Tokyo topology unique Univ unramified zero zeta function