Noncommutative algebraic geometry; Orders on curves and surfaces; Derived categories; Brauer--Severi schemes; Stacky curves and surfaces; Grothendieck ring of varieties
Abstract :
[en] The thesis deals with three topics linked to hereditary orders. First, we compute the class of the Brauer--Severi variety of a hereditary order in the Grothendieck ring of varieties. This leads to heuristics for a decomposition of the bounded derived category of the Brauer--Severi scheme. Second, we construct a semiorthogonal decomposition of the bounded derived category of the hereditary order using categorical absorption introduced by Kuznetsov--Shinder (2023). The last chapter is joint work with Pieter Belmans and Okke van Garderen. We study the restriction of tame orders on surfaces along central curves appealing to a dictionary between orders and stacks, and determine when such a restriction is a hereditary order on a curve. This leads to applications for noncommutative plane curves.
Disciplines :
Mathematics
Author, co-author :
BAUMANN, Thilo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
English
Title :
The geometry of hereditary orders and beyond
Defense date :
20 June 2025
Number of pages :
188
Institution :
Unilu - University of Luxembourg [FSTM], Esch-sur-Alzette, Luxembourg
Degree :
Docteur en Mathématiques (DIP_DOC_0004_B)
Promotor :
SCHEROTZKE, Sarah ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
President :
MERKOULOV, Serguei ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Jury member :
BELMANS, Pieter; UU - Universiteit Utrecht > Mathematical Institute
BOCKLANDT, Raf; UvA - University of Amsterdam > Faculty of Science
BURBAN, Igor; Universität Paderborn > Institut für Mathematik
FnR Project :
FNR12246620 - GPS - Geometry, Probability And Their Synergies, 2017 (01/01/2019-30/06/2025) - Hugo Parlier