Glider Brauer-Severi varieties of central simple algebras

Abstract

The glider Brauer-Severi variety GBS(A) of a central simple algebra A over a field K is introduced as the set of all irreducible left glider ideals in A for some filtration FA. For fields we deduce that GBS(K) equals R(K)×Z, the product of the Riemann surface of K and Z. For a csa A over K it turns out that GBS(A)=BS(A)×GBS(K), where BS(A) denotes the classical Brauer-Severi variety of A.