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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
20
votes
Accepted
Why does Tate's conjecture imply semisimplicity of crystalline Frobenius?
Milne's Remark 8.6 in Amer. J. Math. 1986 implicitely includes two algebraic statements:
Tensor product respects generalised eigenspaces.
Let $V, W$ be representations of a group over a field of cha …