89 citations · 204 across the 10 of their papers we have counts for
12 papers
Two results on the Hodge structure of complex tori
François Charles
We prove two results regarding Hodge structures appearing in the cohomology of complex tori. First, we prove that if a polarizable Hodge structure appears in the cohomology of a co…
Families of rational curves on holomorphic symplectic varieties and applications to zero-cycles
François Charles, Giovanni Mongardi, Gianluca Pacienza
We study families of rational curves on irreducible holomorphic symplectic varieties. We give a necessary and sufficient condition for a sufficiently ample linear system on a holom…
A remark on uniform boundedness for Brauer groups
Anna Cadoret, François Charles
The Tate conjecture for divisors on varieties over number fields is equivalent to finiteness of -primary torsion in the Brauer group. We show that this finiteness is actually…
Birational boundedness for holomorphic symplectic varieties, Zarhin's trick for surfaces, and the Tate conjecture
François Charles
We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick by for surfaces by co…
Families of rational curves on holomorphic symplectic varieties and applications to 0-cycles
François Charles, Gianluca Pacienza
We study families of rational curves on certain irreducible holomorphic symplectic varieties. In particular, we prove that any ample linear system on a projective holomorphic sympl…
Bertini irreducibility theorems over finite fields
François Charles, Bjorn Poonen
Given a geometrically irreducible subscheme X in P^n over F_q of dimension at least 2, we prove that the fraction of degree d hypersurfaces H such that the intersection of H and X…