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Generation in Geometric Derived Cate...

Khromenkov, Yaroslav.

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Generation in Geometric Derived Categories.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Generation in Geometric Derived Categories./
Author:	Khromenkov, Yaroslav.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
Description:	55 p.
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30568171
ISBN:	9798380144674

Generation in Geometric Derived Categories.
Khromenkov, Yaroslav.

Generation in Geometric Derived Categories. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 55 p.

Source: Dissertations Abstracts International, Volume: 85-02, Section: B.

Thesis (Ph.D.)--Northwestern University, 2023.

The main topic of this thesis is generation in derived categories of coherent sheaves on smooth projective varieties. We develop a new approach that allows us to give a new proof of a recent result by Olander that powers of an ample line bundle generate the bounded derived category of coherent sheaves on a smooth projective variety X of dimension n in n steps, we also provide an effective bound on the power of the ample line bundle needed to generate the bounded derived category of coherent sheaves on X in 2n - 1 steps. We also show that for a smooth projective toric variety X of dimension n over an arbitrary algebraically closed field, the Rouquier dimension of the bounded derived category of coherent sheaves on X is less or equal than 2n - 1. We also study derived categories of coherent D-modules on smooth projective varieties. We describe the subcategory of proper objects in the bounded derived category of coherent D-modules on a smooth projective variety X, and as a consequence we obtain that several geometric invariants of X are determined by the bounded derived category of coherent D-modules on X.

ISBN: 9798380144674Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebraic geometry

Generation in Geometric Derived Categories.
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020 $a 9798380144674
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100 1 $a Khromenkov, Yaroslav. $3 3771628
245 1 0 $a Generation in Geometric Derived Categories.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 55 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
500 $a Advisor: Popa, Mihnea;Tamarkin, Dmitry.
502 $a Thesis (Ph.D.)--Northwestern University, 2023.
520 $a The main topic of this thesis is generation in derived categories of coherent sheaves on smooth projective varieties. We develop a new approach that allows us to give a new proof of a recent result by Olander that powers of an ample line bundle generate the bounded derived category of coherent sheaves on a smooth projective variety X of dimension n in n steps, we also provide an effective bound on the power of the ample line bundle needed to generate the bounded derived category of coherent sheaves on X in 2n - 1 steps. We also show that for a smooth projective toric variety X of dimension n over an arbitrary algebraically closed field, the Rouquier dimension of the bounded derived category of coherent sheaves on X is less or equal than 2n - 1. We also study derived categories of coherent D-modules on smooth projective varieties. We describe the subcategory of proper objects in the bounded derived category of coherent D-modules on a smooth projective variety X, and as a consequence we obtain that several geometric invariants of X are determined by the bounded derived category of coherent D-modules on X.
590 $a School code: 0163.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Algebraic geometry
653 $a Derived categories
653 $a Rouquier dimension
653 $a Dimension
653 $a D-modules
690 $a 0405
690 $a 0642
710 2 $a Northwestern University. $b Mathematics. $3 1280008
773 0 $t Dissertations Abstracts International $g 85-02B.
790 $a 0163
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30568171