Ten problems on quadratic forms
The image of the natural homomorphism of Witt rings of orders in a global field
Let R be a Dedekind domain whose field of fractions is a global field. Moreover, let 𝓞 < R be an order. We examine the image of the natural homomorphism φ : W𝓞 → WR of the corresponding Witt rings. We formulate necessary and sufficient conditions for the surjectivity of φ in the case of all nonreal quadratic number fields, all real quadratic number fields K such that -1 is a norm in the extension K/ℚ, and all quadratic function fields.
The intersection theorem for orderings of higher level in rings.
The Noether-Lefschetz theorem and sums of 4 squares in the rational function field
The quadratic form transfer and valuations.
The reduced Wittring
The Witt ring of an elliptic curve over a local field.
Trace forms of central simple algebras.
Trivialization of fans in planar ternary rings with rational prime field.
Twisted Pfister forms.