## Hodge Cycles, Motives, and Shimura Varieties, Issue 900 (Google eBook)This volume collects six related articles. The first is the notes (written by J.S. Milne) of a major part of the seminar "Periodes des Int~grales Abeliennes" given by P. Deligne at I'.B.E.S., 1978-79. The second article was written for this volume (by P. Deligne and J.S. Milne) and is largely based on: N Saavedra Rivano, Categories tannakiennes, Lecture Notes in Math. 265, Springer, Heidelberg 1972. The third article is a slight expansion of part of: J.S. Milne and Kuang-yen Shih, Sh~ura varieties: conjugates and the action of complex conjugation 154 pp. (Unpublished manuscript, October 1979). The fourth article is based on a letter from P. De1igne to R. Langlands, dated 10th April, 1979, and was revised and completed (by De1igne) in July, 1981. The fifth article is a slight revision of another section of the manuscript of Milne and Shih referred to above. The sixth article, by A. Ogus, dates from July, 1980. |

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### Contents

9 | |

101 | |

229 | |

IV MOTIFS ET GROUPES DE TANIYAMA | 261 |

J S Milne and Ky Shih | 280 |

VI Hodge Cycles and Crystalline Cohomology | 357 |

### Common terms and phrases

abelian tensor category abelian type abelian varieties absolute Hodge cycle absolutely Tate action affine group scheme algebraic cycle algebraic group algebraically closed algébrique assume automorphism bilinear canonical isomorphism canonical model characteristic zero choose CM-type cohomology class commutative compatible complex conjecture CM conjugate Corollary corresponding crystalline cohomology decomposition defined défini Deligne denote diagram dimension embedding End(l End(X equivalence exists fibre functor filtration finite Galois extension finite-dimensional fixed follows Frobenius G-torsor Galois extension gerb GL(V group scheme hence Hodge structure homomorphism implies induces inverse isomorphism k-algebra k-linear Lemma lemme Let G Math morphism motivic Galois group Mumford-Tate group ob(C object pair polarization Proof Proposition prove quotient Remark representation of G Saavedra semisimple Serre group Shimura varieties shows smooth spec subgroup subspace surjective Taniyama group Tannakian category Tate triple tensor category tensor functor theorem torsor torus trivial type CM unique vector space