Admissible subcategories of noncommutative curves

Fuente: arXiv
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Main Author: Robotis, Antonios-Alexandros
Format: Preprint
Published: 2023
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author Robotis, Antonios-Alexandros
author_facet Robotis, Antonios-Alexandros
contents We study admissible subcategories of the derived categories of smooth noncommutative (nc) curves as classified by Reiten-van den Bergh. We prove that any admissible subcategory of the derived category of a smooth nc curve is again the derived category of a smooth nc curve. We use this result to classify semiorthogonal decompositions in derived categories of nc curves. The results obtained imply that phantom categories do not exist in these cases. As a further application, we prove an extension of the Bondal-Orlov reconstruction theorem to the case of orbifold curves.
format Preprint
id arxiv_https___arxiv_org_abs_2312_06967
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Admissible subcategories of noncommutative curves
Robotis, Antonios-Alexandros
Algebraic Geometry
Category Theory
Representation Theory
14A30 18G80
We study admissible subcategories of the derived categories of smooth noncommutative (nc) curves as classified by Reiten-van den Bergh. We prove that any admissible subcategory of the derived category of a smooth nc curve is again the derived category of a smooth nc curve. We use this result to classify semiorthogonal decompositions in derived categories of nc curves. The results obtained imply that phantom categories do not exist in these cases. As a further application, we prove an extension of the Bondal-Orlov reconstruction theorem to the case of orbifold curves.
title Admissible subcategories of noncommutative curves
topic Algebraic Geometry
Category Theory
Representation Theory
14A30 18G80
url https://arxiv.org/abs/2312.06967