9 citations · 19 across the 22 of their papers we have counts for
6 papers · 1 filter
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…
A ruled residue theorem for function fields of elliptic curves
Karim Johannes Becher, Parul Gupta, Sumit Chandra Mishra
It is shown that a valuation of residue characteristic different from and on a field has at most one extension to the function field of an elliptic curve over , for…
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…
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 $(…
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…