Chow Groups of Conic Bundle Surfaces

摘要

A characteristic map of the group of 0-dimensional cycles of degree zero module rational equivalence into the first cohomology's product group (conic bundle surface by algebraic closure of a perfect field) tensor product non zero members of algebric closure, is described. The characteristic map is related to a map of the norm group into a product of the norm groups corresponding to the points of a Severi-Braver k-curve where the quaternion K-algebra corresponding to the generic fiber ramifies. The characteristic map of the Chow group for tonic bundle surfaces is described.