Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

One-motives and a conjecture of Deligne


Author: Niranjan Ramachandran
Journal: J. Algebraic Geom. 13 (2004), 29-80
DOI: https://doi.org/10.1090/S1056-3911-03-00370-9
Published electronically: September 22, 2003
MathSciNet review: 2008715
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Abstract | References | Additional Information

Abstract: We introduce new motivic invariants of arbitrary varieties over a perfect field. These cohomological invariants take values in the category of one-motives (considered up to isogeny in positive characteristic). The algebraic definition of these invariants presented here proves a conjecture of Deligne. Other applications include some cases of conjectures of Serre, Katz, and Jannsen on the independence of $\ell$ of parts of the étale cohomology of arbitrary varieties over number fields and finite fields.


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Additional Information

Niranjan Ramachandran
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Email: atma@math.umd.edu

DOI: https://doi.org/10.1090/S1056-3911-03-00370-9
Received by editor(s): May 7, 2001
Received by editor(s) in revised form: September 20, 2002
Published electronically: September 22, 2003
Additional Notes: Funded in part by grants from Hewlett-Packard, Graduate Research Board (UMD), and MPIM (Bonn)
Dedicated: Dedicated to my parents