## Computing Chow groups.(English)Zbl 0663.14001

Algebraic geometry, Proc. Conf., Sundance/Utah 1986, Lect. Notes Math. 1311, 220-234 (1988).
[For the entire collection see Zbl 0635.00006.]
Let X be an algebraic k-scheme of finite type with a cellular decomposition $$\{Z_{ij}\}$$ as defined by W. Fulton [(“Intersection theory” (Berlin 1984; Zbl 0541.14005)] and k an algebraically closed field. The authors give a description of the Chow groups of X, they show that they are free with basis the closure of the cells of the decomposition, in any characteristic. In the case of a fibration $$f:\quad X'\to X,$$ such that $$f^{-1}(Z_{ij})=Z_{ij}\times F$$ where F is a fixed scheme, they give a method to compute the Chow groups of X’ in terms of the Chow groups of X and F.
Reviewer: A.Papantonopoulou

### MSC:

 14C05 Parametrization (Chow and Hilbert schemes) 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14D99 Families, fibrations in algebraic geometry

### Keywords:

Intersection; Chow groups; fibration

### Citations:

Zbl 0635.00006; Zbl 0541.14005