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

5 votes
1 answer
374 views

A simplified proof of a BSD inequality in char $p$?

One of the main results of the BSD conjecture in characteristic $p>0$ is the fact that the algebraic rank is less or equal than the analytic rank and that there is an equality iff the $\ell$-torsion ( …
Sylvain Lefuste's user avatar
5 votes
1 answer
636 views

Brauer group of a product of curves

By a famous theorem of Tate, we know that the Tate conjecture holds for a product of curves over a finite field. But this implies that the Brauer group of a product of curves (over finite field) is f …
Sylvain Lefuste's user avatar