3 papers
math.NT2025
Arithmetic Duality
James S. Milne
In the 1950s and 1960s Tate proved some duality theorems in the Galois cohomology of finite modules and abelian varieties. As for most of Tate's work this has had a profound influe…
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…
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…