Quadratic Forms, Local-Global Principles, and Field Invariants- [electronic resource]
Quadratic Forms, Local-Global Principles, and Field Invariants- [electronic resource]
- 자료유형
- 학위논문파일 국외
- 최종처리일시
- 20240214100323
- ISBN
- 9798379755805
- DDC
- 510
- 서명/저자
- Quadratic Forms, Local-Global Principles, and Field Invariants - [electronic resource]
- 발행사항
- [S.l.]: : University of Pennsylvania., 2023
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2023
- 형태사항
- 1 online resource(138 p.)
- 주기사항
- Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
- 주기사항
- Advisor: Harbater, David.
- 학위논문주기
- Thesis (Ph.D.)--University of Pennsylvania, 2023.
- 사용제한주기
- This item must not be sold to any third party vendors.
- 초록/해제
- 요약The Hasse-Minkowski Theorem states that a quadratic form defined over a global field is isotropic if and only if it is isotropic over all completions of the field, and is one of the first examples of a local-global principle for quadratic forms. In this thesis, we investigate local-global principles for quadratic forms over more general fields and their use in answering several questions about quadratic forms. First, we study the validity of the local-global principles for isotropy and isometry of quadratic forms over finitely generated field extensions with respect to various sets of discrete valuations. Next, we use the local-global principle for isotropy to study anisotropic universal quadratic forms, particularly over semi-global fields. Finally, we use the Witt index to ask refined questions about the local-global principle for isotropy and about universal quadratic forms.
- 일반주제명
- Mathematics.
- 일반주제명
- Theoretical mathematics.
- 키워드
- Field invariants
- 키워드
- Quadratic forms
- 기타저자
- University of Pennsylvania Mathematics
- 기본자료저록
- Dissertations Abstracts International. 84-12B.
- 기본자료저록
- Dissertation Abstract International
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.