Regular homomorphisms, with a twist

Abstract: Let $X$ be a smooth projective variety over a field. If the field is $\mathbb C$, Griffiths associates to $X$ an algebraic intermediate Jacobian $J$, which is a complex abelian variety which captures some information about pointed families of algebraic cycles on $X$. More generally, a regular homomorphism to an abelian variety accomplishes something similar for pointed families of algebraic cycles on a variety over any perfect field.

For families of cycles which don't admit a point over the field of definition, we obtain instead a map to a torsor under that abelian variety. I'll explain these results and what they tell us about the rationality of certain threefolds. (Joint work with Sebastian Casalaina-Martin and Charles Vial.)

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar