Chow Groups of Quadrics in Characteristic Two

Chow groups of quadrics and index reduction formula

We show that the Chow group Ch of a non-singular projective quadric has no torsion if dimension of the quadric is greater than 10 (while a non-trivial torsion appears for a certain 10-dimensional quadric over a suitable field). We apply the same method (based on an index reduction formula) to Ch too and show that it is torsionfree if dimension of the quadric is greater than 22. Let F be a field...

Motives and Chow Groups of Quadrics with Application to the U-invariant (after Oleg Izhboldin)

Birational geometry of quadrics in characteristic 2

The theory of quadratic forms can be regarded as studying an important special case of the general problem of birational classification of algebraic varieties. A typical example of a Fano fibration in minimal model theory is a quadric bundle, which can be viewed without loss of information as a quadric hypersurface over the function field of the base variety. This description feeds the problem ...

Chow Groups, Chow Cohomology, and Linear Varieties

We compute the Chow groups and Fulton–MacPherson’s operational Chow cohomology ring for a class of singular rational varieties including toric varieties. The computation is closely related to the weight filtration on the ordinary cohomology of these varieties. We use the computation to answer one of the open problems about operational Chow cohomology: it does not have a natural map to ordinary ...

Characteristic classes in the Chow ring

Let G be a reductive algebraic group over an algebraically closed field k. An algebraic characteristic class of degree i for principal G-bundles on schemes is a function c assigning to each principal G-bundle E → X an element c(E) in the Chow group AX, natural with respect to pullbacks. These classes are analogous to topological characteristic classes (which take values in cohomology), and two ...