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math.AG2025
On the integral Tate conjecture for abelian varieties
J. S. Milne
Recently Engel et al. (2025) have shown that the integral Hodge conjecture fails for very general abelian varieties. Using Deligne's theory of absolute Hodge cycles, we deduce a si…
math.AG2025
Abelian motives and Shimura varieties in nonzero characteristic
James S. Milne
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…