Codimension 2 Cycles on Severi-brauer Varieties

Cycles De Codimension 2 Sur Produits De Variétés De Severi-brauer

Torsion in CH of Severi-Brauer varieties and indecomposability of generic algebras

We compute degrees of algebraic cycles on certain Severi-Brauer varieties and apply it to show that: a generic division algebra of index p and exponent p is not decomposable (in a tensor product of two algebras) for any prime p and any α except the case when p = 2 and 2 | α; the 2-codimensional Chow group CH of the Severi-Brauer variety corresponding to the generic division algebra of index 8 a...

Codimension 2 Cycles on Products of Projective Homogeneous Surfaces

In the present paper, we provide general bounds for the torsion in the codimension 2 Chow groups of the products of projective homogeneous surfaces. In particular, we determine the torsion for the product of four Pfister quadric surfaces and the maximal torsion for the product of three Severi-Brauer surfaces. We also find an upper bound for the torsion of the product of three quadric surfaces w...

Morphisms to Brauer–severi Varieties, with Applications to Del Pezzo Surfaces

We classify morphisms from proper varieties to Brauer– Severi varieties, which generalizes the classical correspondence between morphisms to projective space and globally generated invertible sheaves. As an application, we study del Pezzo surfaces of large degree with a view towards Brauer–Severi varieties, and recover classical results on rational points, the Hasse principle, and weak approxim...

On the Torsion of Chow Groups of Severi-brauer Varieties

In this paper, we generalize a result of Karpenko on the torsion in the second quotient of the gamma filtration for Severi-Brauer varieties to higher degrees. As an application, we provide a nontrivial torsion in higher Chow groups and the topological filtration of the associated generic variety and obtain new upper bounds for the annihilators of the torsion subgroups in the Chow groups of a la...