Hodge Cycles, Motives, and Shimura Varieties

ISBN-13: 9783540111740 / Angielski / Miękka / 1982 / 417 str.

Pierre Deligne; James S. Milne

Opis

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 (Unpublished manuscript, October 1979).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.

Spis treści

General Introduction.- Notations and Conventions.- Hodge Cycles on Abelian Varieties.- Tannakian Categories.- Langlands’s Construction of the Taniyama Group.- Motifs et Groupes de Taniyama.- Conjugates of Shimura Varieties.- Hodge Cycles and Crystalline Cohomology.- Addendum 1989.- General Introduction.- Notations and Conventions.- Hodge Cycles on Abelian Varieties.- Tannakian Categories.- Langlands’s Construction of the Taniyama Group.- Motifs et Groupes de Taniyama.- Conjugates of Shimura Varieties.- Hodge Cycles and Crystalline Cohomology.