7 citations · 9 across the 6 of their papers we have counts for
9 papers
Quasilinear quadratic forms and function fields of quadrics
Stephen Scully
Let and be anisotropic quadratic forms of dimension over a field . In a recent article, we formulated a conjecture describing the general constraints which the…
Hyperbolicity and near hyperbolicity of quadratic forms over function fields of quadrics
Stephen Scully
Let and be anisotropic quadratic forms over a field of characteristic , let be the unique non-negative integer such that $2^s < \mathrm{dim}(p) \leq 2^{s+1}…
A bound for the index of a quadratic form after scalar extension to the function field of a quadric
Stephen Scully
Let be an anisotropic quadratic form defined over a general field . In this article, we formulate a new upper bound for the isotropy index of after scalar extension to t…
The Artin-Springer Theorem for quadratic forms over semi-local rings with finite residue fields
Stephen Scully
Let be a commutative and unital semi-local ring in which 2 is invertible. In this note, we show that anisotropic quadratic spaces over remain anisotropic after base change…
Milnor-Witt -groups of local rings
Stefan Gille, Stephen Scully, Changlong Zhong
We introduce Milnor-Witt -groups of local rings and show that the th Milnor-Witt -group of a local ring which contains an infinite field of characteristic not is t…
Hoffmann's conjecture for totally singular forms of prime degree
Stephen Scully
One of the most significant discrete invariants of a quadratic form over a field is its (full) splitting pattern, a finite sequence of integers which describes the possible…