Isotropy over function fields of Pfister forms
نویسندگان
چکیده
منابع مشابه
Isotropy over Function Fields of Pfister Forms
The question of which quadratic forms become isotropic when extended to the function field of a given form is studied. A formula for the minimum dimension of the minimal isotropic forms associated to such extensions is given, and some consequences thereof are outlined. Especial attention is devoted to function fields of Pfister forms. Here, the relationship between excellence concepts and the i...
متن کاملIsotropy of Products of Quadratic Forms over Field Extensions
The isotropy of products of Pfister forms is studied. In particular, an improved lower bound on the value of their first Witt index is obtained. This result and certain of its corollaries are applied to the study of the weak isotropy index (or equivalently, the sublevel) of arbitrary quadratic forms. The relationship between this invariant and the level of the form is investigated. The problem ...
متن کاملAutomorphic Forms and Sums of Squares over Function Fields
We develop some of the theory of automorphic forms in the function field setting. As an application, we find formulas for the number of ways a polynomial over a finite field can be written as a sum of k squares, k ≥ 2. Given a finite field Fq with q odd, we want to determine how many ways a polynomial in Fq[T ] can be written as a sum of k squares. For k ≥ 3 (or k = 2, −1 not a square in Fq), t...
متن کاملA Hasse Principle for Quadratic Forms over Function Fields
We describe the classical Hasse principle for the existence of nontrivial zeros for quadratic forms over number fields, namely, local zeros over all completions at places of the number field imply nontrivial zeros over the number field itself. We then go on to explain more general questions related to the Hasse principle for nontrivial zeros of quadratic forms over function fields, with referen...
متن کاملQuadratic Forms over Arbitrary Fields
Introduction. Witt [5] proved that two binary or ternary quadratic forms, over an arbitrary field (of characteristic not 2) are equivalent if and only if they have the same determinant and Hasse invariant. His proof is brief and elegant but uses a lot of the theory of simple algebras. The purpose of this note is to make this fundamental theorem more accessible by giving a short proof using only...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.03.025