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Potential Modularity of K3 Surfaces ...

Gu, Chao.

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Potential Modularity of K3 Surfaces with Large Picard Rank.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Potential Modularity of K3 Surfaces with Large Picard Rank./
作者:	Gu, Chao.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2023,
面頁冊數:	66 p.
附註:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
標題:	Mathematics. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30521572
ISBN:	9798380140317

Potential Modularity of K3 Surfaces with Large Picard Rank.
Gu, Chao.

Potential Modularity of K3 Surfaces with Large Picard Rank. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 66 p.

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

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

The first part of this thesis studied GSp4 -type abelian varieties and the corresponding compatible systems of GSp4 representations. Techniques in [BCGP21] are applied to show that one can prove the potential modularity of these abelian varieties and compatible systems under some conditions that guarantee a sufficient amount of good primes. Then, in the second part, we use the potential modularity theorems to prove that K3 surfaces over totally real field F with Picard rank ≥ 17 are potentially modular.

ISBN: 9798380140317Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Compatible systems

Potential Modularity of K3 Surfaces with Large Picard Rank.
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020 $a 9798380140317
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035 $a AAI30521572
035 $a 2401522
040 $a MiAaPQ $c MiAaPQ
100 1 $a Gu, Chao. $3 1280543
245 1 0 $a Potential Modularity of K3 Surfaces with Large Picard Rank.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 66 p.
500 $a Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
500 $a Advisor: Calegari, Frank.
502 $a Thesis (Ph.D.)--The University of Chicago, 2023.
520 $a The first part of this thesis studied GSp4 -type abelian varieties and the corresponding compatible systems of GSp4 representations. Techniques in [BCGP21] are applied to show that one can prove the potential modularity of these abelian varieties and compatible systems under some conditions that guarantee a sufficient amount of good primes. Then, in the second part, we use the potential modularity theorems to prove that K3 surfaces over totally real field F with Picard rank ≥ 17 are potentially modular.
590 $a School code: 0330.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Compatible systems
653 $a GSp(4)
653 $a K3 surface
653 $a Potential modularity
653 $a Picard rank
690 $a 0405
690 $a 0642
710 2 $a The University of Chicago. $b Mathematics. $3 2049825
773 0 $t Dissertations Abstracts International $g 85-02B.
790 $a 0330
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30521572