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Results tagged with quadratic-forms
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user 1149
Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
18
votes
2
answers
2k
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History of "no positive definite ternary integral quadratic form is universal"?
I am currently leading a graduate student research group on geometry of numbers (henceforth GoN) and its Diophantine applications, especially to quadratic forms. In an early lecture I gave a bit of a …
- 65.4k
22
votes
3
answers
2k
views
Must a ring which admits a Euclidean quadratic form be Euclidean?
The question is in the title, but employs some private terminology, so I had better explain.
Let $R$ be an integral domain with fraction field $K$, and write $R^{\bullet}$ for $R \setminus \{0\}$. Fo …
- 65.4k
6
votes
1
answer
448
views
If two fields are elementarily equivalent, what can we say about their Witt rings?
The question is in the title exactly as I want to ask it, but let me provide some background and motivation.
Many of the properties of fields studied in the algebraic theory of quadratic forms are ma …
- 65.4k