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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

23 votes
Accepted

Local factors of Hasse-Weil zeta function - what do they have in common?

This is an elaboration on ACL's answer, way too long for a comment, which highlights a technical ingredient (well-known to all experts) that underlies the precise sense in which the $\ell$-adic etale …
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6 votes

Etale cohomology and restricted direct product

You don't define what is meant by ${\rm{H}}^1(\mathfrak{o}_v, A)$ (it is an abuse of notation, as $A$ lives over $k$ or $k_v$, not $\mathfrak{o}_v$), but the only definition which comes to mind at a g …
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