Abelian motives and Shimura varieties in nonzero characteristic

Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences.

Publication Details

Journal
ArXiv.org
Published
2025-08-13
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

Abelian motives and Shimura varieties in nonzero characteristic

ArXiv.org
Algebraic Geometry and Number Theory
article

Abelian motives and Shimura varieties in nonzero characteristic

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Abstract

Much of the work on Shimura varieties over the last thirty years has been devoted to constructing the theory that would follow from a good notion of motives, one incorporating the Hodge, Tate, and standard conjectures. These conjectures are believed to be beyond reach, and may not even be correct as stated. I argue in this article that there exists a theory of motives, accessible to proof, weaker than Grothendieck's, but with many of the same consequences.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 44%
Algebraic Geometry and Number Theory
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Abelian motives and Shimura varieties in nonzero characteristic · ArXiv.org (2025) | TGRS Research Map | TGRS