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Crafting Euler Systems: Beyond the Motivic Mold
Crafting Euler Systems: Beyond the Motivic Mold
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151441
- ISBN
- 9798382807454
- DDC
- 510
- 서명/저자
- Crafting Euler Systems: Beyond the Motivic Mold
- 발행사항
- [Sl] : Princeton University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 434 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Skinner, Christopher.
- 학위논문주기
- Thesis (Ph.D.)--Princeton University, 2024.
- 초록/해제
- 요약This dissertation studies Euler Systems and their arithmetic applications. Euler Systems have proven to be versatile tools for understanding Selmer groups and their connections to special values of L-functions. However, despite their importance in foundational conjectures in number theory like the Bloch-Kato conjecture, only a handful of provably non-trivial Euler systems have been constructed to date.A significant obstacle in constructing Euler Systems lies in producing candidate Galois cohomology classes. This thesis presents a method to overcome this obstacle without relying on rare motivic classes.In joint work with C. Skinner, I use Eisenstein classes on Siegel threefolds to construct a cyclotomic Euler System for the adjoint of an elliptic modular form. I also construct integral absolute etale classes on modular curves associated to theta series at inert primes. These theta classes should give new insight into the Iwasawa main conjecture for modular forms over quadratic imaginary fields at inert primes.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 키워드
- Bloch-Kato
- 키워드
- Euler System
- 키워드
- Iwasawa theory
- 키워드
- Modular forms
- 키워드
- Selmer group
- 기타저자
- Princeton University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211151441
■006m o d
■007cr#unu||||||||
■020 ▼a9798382807454
■035 ▼a(MiAaPQ)AAI31296125
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aSangiovanni Vincentelli, Marco.
■24510▼aCrafting Euler Systems: Beyond the Motivic Mold
■260 ▼a[Sl]▼bPrinceton University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a434 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Skinner, Christopher.
■5021 ▼aThesis (Ph.D.)--Princeton University, 2024.
■520 ▼aThis dissertation studies Euler Systems and their arithmetic applications. Euler Systems have proven to be versatile tools for understanding Selmer groups and their connections to special values of L-functions. However, despite their importance in foundational conjectures in number theory like the Bloch-Kato conjecture, only a handful of provably non-trivial Euler systems have been constructed to date.A significant obstacle in constructing Euler Systems lies in producing candidate Galois cohomology classes. This thesis presents a method to overcome this obstacle without relying on rare motivic classes.In joint work with C. Skinner, I use Eisenstein classes on Siegel threefolds to construct a cyclotomic Euler System for the adjoint of an elliptic modular form. I also construct integral absolute etale classes on modular curves associated to theta series at inert primes. These theta classes should give new insight into the Iwasawa main conjecture for modular forms over quadratic imaginary fields at inert primes.
■590 ▼aSchool code: 0181.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■653 ▼aArithmetic applications
■653 ▼aBloch-Kato
■653 ▼aEuler System
■653 ▼aIwasawa theory
■653 ▼aModular forms
■653 ▼aSelmer group
■690 ▼a0405
■690 ▼a0642
■71020▼aPrinceton University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0181
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161761▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
