國立虎尾科技大學 |

Generation in Geometric Derived Categories.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Generation in Geometric Derived Categories./
作者:	Khromenkov, Yaroslav.
面頁冊數:	1 online resource (55 pages)
附註:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
標題:	Mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9798380144674

Generation in Geometric Derived Categories.
Khromenkov, Yaroslav.

Generation in Geometric Derived Categories. - 1 online resource (55 pages)

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

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

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380144674Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Algebraic geometryIndex Terms--Genre/Form:

554714
Electronic books.

Generation in Geometric Derived Categories.
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500 $a Advisor: Popa, Mihnea;Tamarkin, Dmitry.
502 $a Thesis (Ph.D.)--Northwestern University, 2023.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2024
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Theoretical mathematics. $3 1180455
653 $a Algebraic geometry
653 $a Derived categories
653 $a Rouquier dimension
653 $a Dimension
653 $a D-modules
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