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Monodromy Results for Abelian Surfac...

Bhatnagar, Tejasi,

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Monodromy Results for Abelian Surfaces and K3 Surfaces in Characteristic p /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Monodromy Results for Abelian Surfaces and K3 Surfaces in Characteristic p // Tejasi Bhatnagar.
作者:	Bhatnagar, Tejasi,
面頁冊數:	1 electronic resource (44 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-10, Section: B.
Contained By:	Dissertations Abstracts International86-10B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31997179
ISBN:	9798314806869

Monodromy Results for Abelian Surfaces and K3 Surfaces in Characteristic p /
Bhatnagar, Tejasi,

Monodromy Results for Abelian Surfaces and K3 Surfaces in Characteristic p /Tejasi Bhatnagar. - 1 electronic resource (44 pages)

Source: Dissertations Abstracts International, Volume: 86-10, Section: B.

In this thesis, we generalise a p-adic monodromy theorem of Igusa to orthogonal Shimura varieties in characteristic p. Igusa's theorem studies the monodromy representation associated to the universal elliptic curve around a supersingular point of the modular curve. We prove an analogous result for the monodromy representation associated to an ordinary point of an othogonal Shimura variety that reduces to the boundary. As special cases, we get results for abelian surfaces and K3 surfaces with bad reduction. Moreover, we apply the theorem to prove a finiteness result for the reduction of the Hecke orbit in such a setting.

English

ISBN: 9798314806869Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Abelian varieties

Monodromy Results for Abelian Surfaces and K3 Surfaces in Characteristic p /
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245 1 0 $a Monodromy Results for Abelian Surfaces and K3 Surfaces in Characteristic p / $c Tejasi Bhatnagar.
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300 $a 1 electronic resource (44 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-10, Section: B.
500 $a Advisors: Shankar, Ananth Committee members: Ellenberg, Jordan; Yang, Tonghai; Kent, Autumn.
502 $b Ph.D. $c The University of Wisconsin - Madison $d 2025.
520 $a In this thesis, we generalise a p-adic monodromy theorem of Igusa to orthogonal Shimura varieties in characteristic p. Igusa's theorem studies the monodromy representation associated to the universal elliptic curve around a supersingular point of the modular curve. We prove an analogous result for the monodromy representation associated to an ordinary point of an othogonal Shimura variety that reduces to the boundary. As special cases, we get results for abelian surfaces and K3 surfaces with bad reduction. Moreover, we apply the theorem to prove a finiteness result for the reduction of the Hecke orbit in such a setting.
546 $a English
590 $a School code: 0262
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Applied mathematics. $3 2122814
653 $a Abelian varieties
653 $a Arithmetic geometry
653 $a Number theory
653 $a Shimura varieties
690 $a 0405
690 $a 0642
690 $a 0364
710 2 $a The University of Wisconsin - Madison. $b Mathematics. $e degree granting institution. $3 3823099
720 1 $a Shankar, Ananth $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-10B.
790 $a 0262
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31997179