A Filtration of the Chow Group of Zero-Cycles for a Product of Curves and an Abelian Variety. Submitted (32 pages).
In this paper, we define a descending filtration on the Chow group of zero cycles for smooth projective varieties which are the product of curves and an abelian variety. We give explicit generators and relations for the successive quotients of this filtration by showing that they can be described by Somekawa K-groups. This extends the work of Raskind and Spiess who proved this result for products of curves and Gazaki who proved this for abelian varieties.
Chow groups of Enriques surfaces over p-adic fields
By the work of Bloch, Kas, and Lieberman, the degree zero subgroup of the Chow group of zero-cycles for an Enriques surface over an algebraically closed field of characteristic 0 is trivial. In this project, we study these groups over p-adic fields. We want to find an upper bound on the exponent of these groups as well as find explicit examples where these groups are nonzero. In order to produce such examples, our goal is to make use of the Brauer-Manin pairing, as well as known results on the Brauer group of Enriques surfaces.