A Recursive Description of the Maximal Pro-2 Galois Group Via Witt Rings.
A Remark on Kitaoka formal power series attached to local densities.
Effective version of Tartakowsky's Theorem
Eine Bemerkung über quadratische Formen über einem lokalem Ring der Charakteristik 2.
Euclidean quadratic forms and ADC forms: I
Euclidean quadratic forms and ADC forms II: integral forms
We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.
Formes p-adiques anisotropes.
Formes quadratiques sur les anneaux semi-locaux réguliers
Indecomposable integral quadratic forms over global function fields
Integral spinor norms in dyadic local fields II
Isotropy of quadratic forms over function fields of -adic curves
Le groupe des classes module 2 d'après Conner et Perlis.
Levels of rings - a survey
Let R be a ring with 1 ≠ 0. The level s(R) of R is the least integer n such that -1 is a sum of n squares in R provided such an integer exists, otherwise one defines the level to be infinite. In this survey, we give an overview on the history and the major results concerning the level of rings and some related questions on sums of squares in rings with finite level. The main focus will be on levels of fields, of simple noncommutative rings, in particular division rings, and of arbitrary commutative...
Local conditions for global representations of quadratic forms
Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains
Let be a 2-dimensional normal excellent henselian local domain in which is invertible and let and be its fraction field and residue field respectively. Let be the set of rank 1 discrete valuations of corresponding to codimension 1 points of regular proper models of . We prove that a quadratic form over satisfies the local-global principle with respect to in the following two cases: (1) has rank 3 or 4; (2) has rank and , where is a complete discrete valuation ring with...
On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings
Harbater, Hartmann and Krashen obtained in 2015 a criterion for the existence of rational points on projective (or principal) homogeneous varieties for rational connected algebraic groups defined over function fields of normal curves over a complete discrete valuation ring in terms of completions of local rings at special points. This was obtained by a reduction via Artin approximation to a related patching problem solved by the same authors in 2009. In the special case of projective quadrics, we...
On systems of three quadratic forms
On the classification of quadratic forms over semi local rings
On the intersection of modular correspondences.
Orderings of Higher Level and Semilocal Rings.