Lefschetz Motives and the Tate Conjecture
dc.contributor.author | Milne, J. S. | en_US |
dc.date.accessioned | 2006-09-08T20:30:56Z | |
dc.date.available | 2006-09-08T20:30:56Z | |
dc.date.issued | 1999-05 | en_US |
dc.identifier.citation | Milne, J. S.; (1999). "Lefschetz Motives and the Tate Conjecture." Compositio Mathematica 117(1): 47-81. <http://hdl.handle.net/2027.42/42599> | en_US |
dc.identifier.issn | 0010-437X | en_US |
dc.identifier.issn | 1570-5846 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/42599 | |
dc.description.abstract | A Lefschetz class on a smooth projective variety is an element of the Q-algebra generated by divisor classes. We show that it is possible to define Q-linear Tannakian categories of abelian motives using the Lefschetz classes as correspondences, and we compute the fundamental groups of the categories. As an application, we prove that the Hodge conjecture for complex abelian varieties of CM-type implies the Tate conjecture for all Abelian varieties over finite fields, thereby reducing the latter to a problem in complex analysis. | en_US |
dc.format.extent | 283083 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; Springer Science+Business Media | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Mathematics, General | en_US |
dc.subject.other | Abelian Varieties | en_US |
dc.subject.other | Tate Conjecture | en_US |
dc.subject.other | Motives. | en_US |
dc.title | Lefschetz Motives and the Tate Conjecture | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109–1109, U.S.A. e-mail | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/42599/1/10599_2004_Article_156511.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1023/A:1000776613765 | en_US |
dc.identifier.source | Compositio Mathematica | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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