Abelian motives and Shimura varieties in nonzero characteristic

2025/08/13 by Milne, James S. · 1 citation
#14C15 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.09972

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.

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