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Quadratic Forms, Local-Global Principles, and Field Invariants / Connor Dane Cassady.
- Format:
- Book
- Thesis/Dissertation
- Author/Creator:
- Cassady, Connor Dane, author.
- Language:
- English
- Subjects (All):
- Mathematics.
- Theoretical mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Local Subjects:
- Mathematics.
- Theoretical mathematics.
- Mathematics--Penn dissertations.
- Penn dissertations--Mathematics.
- Physical Description:
- 1 online resource (138 pages)
- Distribution:
- Ann Arbor : ProQuest Dissertations & Theses, 2023
- Contained In:
- Dissertations Abstracts International 84-12B.
- Place of Publication:
- [Philadelphia, Pennsylvania] : University of Pennsylvania, 2022.
- Language Note:
- English
- Summary:
- The 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.
- Notes:
- Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
- Advisors: Harbater, David; Committee members: Hartmann, Julia; Haglund, James.
- Department: Mathematics.
- Ph.D. University of Pennsylvania 2023.
- Local Notes:
- School code: 0175
- ISBN:
- 9798379755805
- Access Restriction:
- Restricted for use by site license.
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