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math.AG2018★ 5 cited
Normal functions for algebraically trivial cycles are algebraic for arithmetic reasons
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For families of smooth complex projective varieties we show that normal functions arising from algebraically trivial cycle classes are algebraic, and defined over the field of defi…
math.AG2018★ 2 cited
Generic cycles, Lefschetz representations, and the generalized Hodge and Bloch conjectures for abelian varieties
Charles Vial
We prove Bloch's conjecture for correspondences on powers of complex abelian varieties, that are "generically defined". As an application we establish vanishing results for (skew-)…