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A Non-Archimedean Definable Chow The...

Oswal, Abhishek Bharat.

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A Non-Archimedean Definable Chow Theorem.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A Non-Archimedean Definable Chow Theorem./
作者:	Oswal, Abhishek Bharat.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
面頁冊數:	64 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-06, Section: B.
Contained By:	Dissertations Abstracts International82-06B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28025035
ISBN:	9798698545859

A Non-Archimedean Definable Chow Theorem.
Oswal, Abhishek Bharat.

A Non-Archimedean Definable Chow Theorem. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 64 p.

Source: Dissertations Abstracts International, Volume: 82-06, Section: B.

Thesis (Ph.D.)--University of Toronto (Canada), 2020.

This item must not be sold to any third party vendors.

O-minimality has had some striking applications to number theory. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this thesis, we explore a non-archimedean analogue of an o-minimal structure and prove a version of the definable Chow theorem in this context.

ISBN: 9798698545859Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Non-Archimedean theorem

A Non-Archimedean Definable Chow Theorem.
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500 $a Source: Dissertations Abstracts International, Volume: 82-06, Section: B.
500 $a Advisor: Tsimerman, Jacob.
502 $a Thesis (Ph.D.)--University of Toronto (Canada), 2020.
506 $a This item must not be sold to any third party vendors.
520 $a O-minimality has had some striking applications to number theory. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this thesis, we explore a non-archimedean analogue of an o-minimal structure and prove a version of the definable Chow theorem in this context.
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