23 citations · 34 across the 15 of their papers we have counts for
4 papers · 2 filters
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…
Universal quadratic forms and Northcott property of infinite number fields
Nicolas Daans, Vítězslav Kala, Siu Hang Man
We show that if a universal quadratic form exists over an infinite degree, totally real extension of the field of rationals , then the set of totally positive integers…
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 $(…
Universally defining in with quantifiers
Nicolas Daans
We show that for a global field , every ring of -integers has a universal first-order definition in with quantifiers. We also give a proof that every finite intersec…