A remark on uniform boundedness for Brauer groups

الأصل · EN

The Tate conjecture for divisors on varieties over number fields is equivalent to finiteness of ℓ-primary torsion in the Brauer group. We show that this finiteness is actually uniform in one-dimensional families for varieties that satisfy the Tate conjecture for divisors -- e.g. abelian varieties and K3 surfaces.