# Glider Brauer-Severi varietes of central simple algebras

## TL;DR

This paper introduces the concept of glider Brauer-Severi varieties for central simple algebras, linking algebraic structures with geometric objects and extending classical theory.

## Contribution

It defines the glider Brauer-Severi variety for central simple algebras and establishes its relation to classical Brauer-Severi varieties and the Riemann surface of the base field.

## Key findings

- GBS(K) equals R(K) x Z for fields
- GBS(A) equals BS(A) x GBS(K) for central simple algebras
- Connects algebraic ideals with geometric varieties

## Abstract

The glider Brauer-Severy 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 the ring of integers 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.