5 papers · 1 filter
Regular homomorphisms, with a twist
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
Let be a variety over a field, and an abelian variety. A regular homomorphism to (in codimension ) induces, for every smooth geometrically connected pointed -…
Decomposition of the diagonal, intermediate Jacobians, and universal codimension-2 cycles in positive characteristic
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
We consider the connections among algebraic cycles, abelian varieties, and stable rationality of smooth projective varieties in positive characteristic. Recently Voisin constructed…
Putting the p back in Prym
Jeff Achter, Sebastian Casalaina-Martin
After Jacobians of curves, Prym varieties are perhaps the next most studied abelian varieties. They turn out to be quite useful in a number of contexts. For technical reasons, ther…
Images of abelian schemes
Jeff Achter, Sebastian Casalaina-Martin, Jonathan Wise
We provide some conditions for the image of a morphism of abelian schemes to again be an abelian scheme. For context, in characteristic 0, the image is always an abelian scheme; in…
A complete answer to Albanese base change for incomplete varieties
Jeff Achter, Sebastian Casalaina-Martin, Charles Vial
Albanese varieties provide a standard tool in algebraic geometry for converting questions about varieties in general, to questions about Abelian varieties. A result of Serre provid…