6 papers
The Walker Abel-Jacobi map descends
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For a complex projective manifold, Walker has defined a regular homomorphism lifting Griffiths' Abel-Jacobi map on algebraically trivial cycle classes to a complex abelian variety,…
On the image of the second l-adic Bloch map
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
For a smooth projective geometrically uniruled threefold defined over a perfect field we show that there exists a canonical abelian variety over the field, namely the second algebr…
Zero-cycles on double EPW sextics
Robert Laterveer, Charles Vial
The Chow rings of hyperKähler varieties are conjectured to have a particularly rich structure. In this paper, we focus on the locally complete family of double EPW sextics and esta…
A motivic global Torelli theorem for isogenous K3 surfaces
Lie Fu, Charles Vial
We prove that the Chow motives of twisted derived equivalent K3 surfaces are isomorphic, not only as Chow motives (due to Huybrechts), but also as Frobenius algebra objects. Combin…
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…
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-)…