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Severi-Brauer varieties; a geometric treatment

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arxiv 1606.04368 v2 pith:JTL3B74K submitted 2016-06-14 math.AG math.NT

János Kollár (Princeton Univ) This is my paper · ORCID
classification math.AGmath.NT
keywords geometricseveri-brauertreatmentvarietiesalgebrascentralcohomologygalois
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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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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Birational equivalence of Severi-Brauer varieties

    math.AG 2025-05 accept novelty 8.0 of 10

    Amitsur's conjecture on birational equivalence of Severi-Brauer varieties is proved whenever the index is not a prime power.

  2. General position on Severi--Brauer surfaces

    math.AG 2026-06 unverdicted novelty 7.0 of 10

    Generalizes the general position condition for del Pezzo surfaces from the projective plane to Severi-Brauer surfaces over arbitrary fields using Galois descent.

  3. Birational Geometry of sextic del Pezzo surfaces

    math.AG 2025-07 accept novelty 7.0 of 10

    Degree 6 del Pezzo surfaces over perfect fields are classified biregularly and birationally, and are shown to be the only solid surfaces admitting infinite pliability, with explicit presentations for their birational ...

  4. Composition of Sarkisov links between del Pezzo surfaces

    math.AG 2026-07 conditional novelty 6.0 of 10

    Over any perfect field, two birationally equivalent del Pezzo surfaces of Picard rank one are connected by a birational map that factors into at most two Sarkisov links, and this bound is optimal.

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