9 citations · 19 across the 22 of their papers we have counts for
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Totally decomposable algebras with involution and R-triviality
M. Archita, Karim Johannes Becher
We show that the group of proper projective similitudes of a totally decomposable algebra with orthogonal or symplectic involution of index at most 2 over a field of characteristic…
Fields with bounded Brauer -torsion index
Karim Johannes Becher
It is shown that, over a field of characteristic not , the dimension of an anisotropic quadratic Pfister form of trivial total signature is at most twice the dimension of some c…
A bound on the index of exponent- algebras in terms of the -invariant
Karim Johannes Becher, Fatma Kader Bingöl
For a prime number , an integer and a field containing a primitive -th root of unity, the index of central simple -algebras of exponent is bounded in…
The discriminant Pfister form of an algebra with involution of capacity four
Karim Johannes Becher, Nicolas Grenier-Boley, Jean-Pierre Tignol
To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form t…
Splitting quaternion algebras defined over a finite field extension
Karim Johannes Becher, Fatma Kader Bingöl, David B. Leep
We study systems of quadratic forms over fields and their isotropy over 2-extensions. We apply this to obtain particular splitting fields for quaternion algebras defined over a fin…
Totally decomposable quadratic pairs
Karim Johannes Becher, Andrew Dolphin
In this paper we show that a split central simple algebra with quadratic pair which decomposes into a tensor product of quaternion algebras with involution and a quaternion algebra…
Weakly Hyperbolic Involutions
Karim Johannes Becher, Thomas Unger
Pfister's Local-Global Principle states that a quadratic form over a (formally) real field is weakly hyperbolic (i.e. represents a torsion element in the Witt ring) if and only if…