Glider Brauer-Severi varieties of central simple algebras

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) x 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) x GBS(K), where BS(A) denotes the classical Brauer-Severi variety of A. (C) 2020 Elsevier Inc. All rights reserved.