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Unlikely Intersections on Shimura Varieties.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Unlikely Intersections on Shimura Varieties./
作者:	G., Asvin.
面頁冊數:	1 online resource (59 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
Contained By:	Dissertations Abstracts International84-11B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30422353click for full text (PQDT)
ISBN:	9798379520991

Unlikely Intersections on Shimura Varieties.
G., Asvin.

Unlikely Intersections on Shimura Varieties. - 1 online resource (59 pages)

Source: Dissertations Abstracts International, Volume: 84-11, Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2023.

Includes bibliographical references

Recently, there has been much work on the question of just-likely intersections on Shimura Varieties. These works are concerned with showing that there are an infinite number of "coincidences" up-to Hecke translations in the case where the dimensions of the subvarieties are complementary. However, all these results only consider intersections between an (arithmetic)curve and a special divisor. A recent AIM project formulated more general conjectures concerning intersections of arbitrary subvarieties in Shimura varieties (up-to Hecke translations) and this thesis takes the first steps towards proving such a general conjecture.In the first part of this thesis, we prove the conjecture (appropriately formulated) for products of the modular curve. Moreover, we also consider unlikely intersections and show that, contrary to expectations, such inter-sections can occur infinitely often in positive characteristic.In the second part of this thesis, in joint work with Qiao He and Ananth Shankar, we prove the conjecture for Hilbert modular surfaces in positive characteristic (with mild restrictions).

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798379520991Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Unlikely intersectionsIndex Terms--Genre/Form:

542853
Electronic books.

Unlikely Intersections on Shimura Varieties.
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500 $a Source: Dissertations Abstracts International, Volume: 84-11, Section: B.
500 $a Advisor: Ellenberg, Jordan.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 2023.
504 $a Includes bibliographical references
520 $a Recently, there has been much work on the question of just-likely intersections on Shimura Varieties. These works are concerned with showing that there are an infinite number of "coincidences" up-to Hecke translations in the case where the dimensions of the subvarieties are complementary. However, all these results only consider intersections between an (arithmetic)curve and a special divisor. A recent AIM project formulated more general conjectures concerning intersections of arbitrary subvarieties in Shimura varieties (up-to Hecke translations) and this thesis takes the first steps towards proving such a general conjecture.In the first part of this thesis, we prove the conjecture (appropriately formulated) for products of the modular curve. Moreover, we also consider unlikely intersections and show that, contrary to expectations, such inter-sections can occur infinitely often in positive characteristic.In the second part of this thesis, in joint work with Qiao He and Ananth Shankar, we prove the conjecture for Hilbert modular surfaces in positive characteristic (with mild restrictions).
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Unlikely intersections
653 $a Shimura varieties
653 $a Arbitrary subvarieties
653 $a Modular surfaces
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690 $a 0642
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