9 citations · 19 across the 22 of their papers we have counts for
12 papers · 1 filter
Fields where torsion forms decompose
M. Archita, Karim Johannes Becher
Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum…
Non--trivial proper projective similitudes in type
M. Archita, Karim Johannes Becher
Over an arbitrary field of characteristic different from admitting an anisotropic torsion -fold Pfister form, we apply a construction due to Merkurjev to produce an algebra…
Similitudes over fields with I^4=0
M. Archita, Karim Johannes Becher
This article studies the set of R-equivalence classes of the group of proper projective similitudes of an algebra with involution of the first kind. The main results concern base f…
Rational connectedness for groups of proper projective similitudes
M. Archita, Karim Johannes Becher
For a quadratic form over a field of characteristic different from , we study whether its group of proper projective similitudes is rationally connected (i…
The u-invariant of function fields in one variable
Karim Johannes Becher, Nicolas Daans, Vlerë Mehmeti
The u-invariant of a field is the largest dimension of an anisotropic quadratic torsion form over the field. In this article we obtain a bound on the u-invariant of function fields…
Bounds on the hermitian u-invariants under quadratic field extensions
Karim Johannes Becher, Fatma Kader Bingöl
The hermitian u-invariants of a central simple algebra with involution are studied. In this context, a new technique is obtained to give bounds for the behavior of these invariants…
Orthogonal involutions over fields with I^3=0
Karim Johannes Becher, Fatma Kader Bingöl
We provide upper bounds on the u-invariant for skew-hermitian forms over a quaternion algebra with its canonical involution in terms of the u-invariant of the base field F of chara…
Uniform existential definitions of valuations in function fields in one variable
Karim Johannes Becher, Nicolas Daans, Philip Dittmann
We study function fields of curves over a base field which is either a global field or a large field having a separable field extension of degree divisible by . We show that…
A comparison of finiteness conditions in quadratic form theory
Karim Johannes Becher, Saurabh Gosavi
We discuss and relate finiteness conditions for certain field invariants which are studied in quadratic form theory. This includes the -invariant, the reduced stability index an…
Sums of squares in function fields over a henselian valued field
Karim Johannes Becher, Nicolas Daans, David Grimm +2
The Pythagoras number of a field is the smallest natural number such that every sum of squares in the field is a sum of squares. Given a nondyadic henselian valued field $(…
Bounding the Pythagoras number of a field by
Karim Johannes Becher, Marco Zaninelli
Given a positive integer , a sufficient condition on a field is given for bounding its Pythagoras number by . The condition is satisfied for by function fields of c…
Nonsplit conics in the reduction of an arithmetic curve
Karim Johannes Becher, David Grimm
For an algebraic function field and a discrete valuation of with perfect residue field , we bound the number of discrete valuations on extending whose resi…