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Potential Modularity of K3 Surfaces with Large Picard Rank.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Potential Modularity of K3 Surfaces with Large Picard Rank./
Author:	Gu, Chao.
Description:	1 online resource (66 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798380140317

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

Potential Modularity of K3 Surfaces with Large Picard Rank. - 1 online resource (66 pages)

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

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

Includes bibliographical references

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.

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

Mode of access: World Wide Web

ISBN: 9798380140317Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Compatible systemsIndex Terms--Genre/Form:

554714
Electronic books.

Potential Modularity of K3 Surfaces with Large Picard Rank.
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504 $a Includes bibliographical references
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.
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538 $a Mode of access: World Wide Web
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650 4 $a Theoretical mathematics. $3 1180455
653 $a Compatible systems
653 $a GSp(4)
653 $a K3 surface
653 $a Potential modularity
653 $a Picard rank
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