Add to ORKGLet A be a complete excellent local domain of Krull dimension 2 and K its field of fractions. We further assume that 2 is invertible in A and that the residue field of A is algebraically closed. We first show that the unramified Brauer group of K (with respect to all discrete valuations of K) vanishes. Using this result we prove that every rank 4 quadratic form which is isotropic in all completions of K with respec
The problem of determining conditions under which a rational map can exist between a pair of twisted...
Let $G$ be an absolutely almost simple algebraic group over a field $K$, which we assume to be equip...
We first recall the classical local class field theory. Let K be a finite extension of Qp or Fq((X))...
Let A be an excellent henselian two-dimensional local domain (for the defi-nition of excellent rings...
If R is a complete discrete valuation ring, then every quadratic space over R[T] is extended from R....
The Hasse-Minkowski theorem says that a quadratic form over a global field admits a nontrivial zero ...
AbstractWe show that dimension 4 quadratic forms over C(t1, t2), ti transcendental, do not satisfy w...
We study which quadratic forms are representable as the local degree of a map $f \colon \mathbb{A}^n...
This thesis is concerned with the study of some arithmetic properties of certain algebraic varieties...
Abstract. Whenever F is a Henselian valued field whose residue class field F has characteristic diff...
Abstract. This paper presents fundamental algorithms for computational theory of quadratic forms ove...
Let k be a field of characteristic different from 2 containing a primitive 4-th root of unity. We sh...
We prove the failure of the local-global principle, with respect to discrete valuations, for isotrop...
It is proved that a quadratic space over the polynomial extension of a global field K is extended fr...
AbstractThe isometry problem is studied for unimodular quadratic forms over the Hasse domains of glo...
The problem of determining conditions under which a rational map can exist between a pair of twisted...
Let $G$ be an absolutely almost simple algebraic group over a field $K$, which we assume to be equip...
We first recall the classical local class field theory. Let K be a finite extension of Qp or Fq((X))...
Let A be an excellent henselian two-dimensional local domain (for the defi-nition of excellent rings...
If R is a complete discrete valuation ring, then every quadratic space over R[T] is extended from R....
The Hasse-Minkowski theorem says that a quadratic form over a global field admits a nontrivial zero ...
AbstractWe show that dimension 4 quadratic forms over C(t1, t2), ti transcendental, do not satisfy w...
We study which quadratic forms are representable as the local degree of a map $f \colon \mathbb{A}^n...
This thesis is concerned with the study of some arithmetic properties of certain algebraic varieties...
Abstract. Whenever F is a Henselian valued field whose residue class field F has characteristic diff...
Abstract. This paper presents fundamental algorithms for computational theory of quadratic forms ove...
Let k be a field of characteristic different from 2 containing a primitive 4-th root of unity. We sh...
We prove the failure of the local-global principle, with respect to discrete valuations, for isotrop...
It is proved that a quadratic space over the polynomial extension of a global field K is extended fr...
AbstractThe isometry problem is studied for unimodular quadratic forms over the Hasse domains of glo...
The problem of determining conditions under which a rational map can exist between a pair of twisted...
Let $G$ be an absolutely almost simple algebraic group over a field $K$, which we assume to be equip...
We first recall the classical local class field theory. Let K be a finite extension of Qp or Fq((X))...