4 citations · 7 across the 6 of their papers we have counts for
6 papers
Large imperfect fields are existentially closed in function fields after finite constant extension
Hagen Knaf, Franz-Viktor Kuhlmann
For an algebraic function field over a large field , we show: 1) if has a rational place, then there is a finite purely inseparable extension such that is…
An Algorithm to Find Rational Points on Elliptic Curves Related to the Concordant Form Problem
Hagen Knaf, Erich Selder, Karlheinz Spindler
We derive an efficient algorithm to find solutions to Euler's concordant form problem and rational points on elliptic curves associated with this problem.
Explicit transformation of an intersection of two quadrics to an elliptic curve in Weierstrass form
Hagen Knaf, Erich Selder, Karlheinz Spindler
This paper, motivated by problems in Diophantine analysis which can be formulated as problems of finding rational points on the intersection of two quadrics, presents an explicit c…
Every place admits local uniformization in a finite extension of the function field
Hagen Knaf, Franz-Viktor Kuhlmann
We prove that every place P of an algebraic function field F|K of arbitrary characteristic admits local uniformization in a finite extension E of F. We show that E|F can be chosen…
Regular local algebras over a Pruefer domain: weak dimension and regular sequences
Hagen Knaf
A not necessarily noetherian local ring O is called regular if every finitely generated ideal I of O possesses finite projective dimension. In the article localizations O of a fini…
Abhyankar places admit local uniformization in any characteristic
Hagen Knaf, Franz-Viktor Kuhlmann
We prove that every place of an algebraic function field of arbitrary characteristic admits local uniformization, provided that the sum of the rational rank of its value…