Severi-Brauer varieties; a geometric treatment
J\'anos Koll\'ar (Princeton Univ)
TL;DR
This paper offers a geometric perspective on Severi-Brauer varieties, avoiding reliance on central simple algebra theory or Galois cohomology, and aims to clarify their structure through geometric methods.
Contribution
It introduces a purely geometric approach to studying Severi-Brauer varieties, providing new insights without using algebraic or cohomological tools.
Findings
Geometric characterization of Severi-Brauer varieties
Simplification of their structural understanding
New proofs avoiding algebraic cohomology
Abstract
These notes present a geometric treatment of Severi-Brauer varieties, without using any results from the theory of central simple algebras or from Galois cohomology. 2026 version: major revisions
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models