共查询到20条相似文献,搜索用时 703 毫秒
1.
Ottmar Loos 《Monatshefte für Mathematik》1996,122(1):45-98
A tensor product for unital quadratic forms is introduced which extends the product of separable quadratic algebras and is naturally associative and commutative. It admits a multiplicative functor vdis, the vector discriminant, with values in symmetric bilinear forms. We also compute the usual (signed) discriminant of the tensor product in terms of the discriminants of the factors. The orthogonal group scheme of a nonsingular unital quadratic formQ of even rank is isomorphic toZ
2×SO(Q
0) whereQ
0 is the restriction of –Q to the space of trace zero elements. We use cohomology to interpret the action of separable quadratic algebras on unital quadratic forms, and to determine which forms of odd rank can be realized asQ
0. 相似文献
2.
The involutions in this paper are algebra anti-automorphisms of period two. Involutions on endomorphism algebras of finite-dimensional
vector spaces are adjoint to symmetric or skew-symmetric bilinear forms, or to hermitian forms. Analogues of the classical
invariants of quadratic forms (discriminant, Clifford algebra, signature) have been defined for arbitrary central simple algebras
with involution. In this paper it is shown that over certain fields these invariants are sufficient to classify involutions
up to conjugation. For algebras of low degree a classification is obtained over an arbitrary field.
Received: 29 April 1999 相似文献
3.
Finiteness of real quadratic fields which admit positive integral diagonal septanary universal forms
Byeong Moon Kim 《manuscripta mathematica》1999,99(2):181-184
In this paper, we will prove if D is large enough, there are no positive integral diagonal septanary universal quadratic forms over .
Received: 13 November 1997 / Revised version: 17 November 1998 相似文献
4.
We construct a 6-dimensional anisotropic quadratic form and a 4-dimensional quadratic form over some fieldF such that becomes isotropic over the function field but every proper subform of is still anisotropic over . It is an example of non-standard isotropy with respect to some standard conditions of isotropy for 6-dimensional forms over function fields of quadrics, known previously.
Besides of that, we produce an 8-dimensional quadratic form with trivial determinant such that the index of the Clifford invariant of is 4 but can not be represented as a sum of two 4-dimensional forms with trivial determinants. Using this, we find a 14-dimensional
quadratic form with trivial discriminant and Clifford invariant, which is not similar to a difference of two 3-fold Pfister
forms. The proofs are based on computations of the topological filtration on the Grothendieck group of certain projective
homogeneous varieties. To do these computations, we develop several methods, covering a wide class of varieties and being,
to our mind, of independent interest.
Received November 11, 1997; in final form June 24, 1999 / Published online May 8, 2000 相似文献
5.
Grégory Berhuy 《Archiv der Mathematik》2007,88(5):434-447
We define a complete system of invariants e
n,Q
,n ≥ 0 for quaternionic skew-hermitian forms, which are twisted versions of the invariants e
n for quadratic forms. We also show that quaternionic skew-hermitian forms defined over a field of 2-cohomological dimension
at most 3 are classified by rank, discriminant, Clifford invariant and Rost invariant.
Received: 30 April 2006 相似文献
6.
Rainer Dietmann 《Monatshefte für Mathematik》2005,146(3):175-178
We obtain new results on linear spaces on the intersection of two quadratic forms defined over a non-dyadic p-adic field
. One of our main tools is a recent result of Parimala and Suresh on isotropy of quadratic forms over functions fields over
. As a corollary we also get new bounds for the number of variables necessary to always find a non-trivial p-adic zero of a system of quadratic forms. 相似文献
7.
Ahmed Laghribi 《Mathematische Zeitschrift》2002,240(4):711-730
In [9] and [10] Knebusch established the basic facts of generic splitting theory of quadratic forms over a field of characteristic
different from 2. This paper is related to [11] and [13] where Knebusch and Rehmann generalized partially this theory to a
field of characteristic 2. More precisely, we begin with a complete characterization of quadratic forms of height 1 (we don't
exclude anisotropic quadratic forms with quasi-linear part of dimension at least 1). This allows us to extend the notion of
degree to characteristic 2. We prove some results on excellent forms and splitting tower of a quadratic form. Some results
on quadratic forms of height 2 and degree 1 or 2 are given.
Received: 6 March 2000; in final form: 5 October 2001 / Published online: 17 June 2002 相似文献
8.
Summary This paper adds the finishing touches to an algorithmic treatment of quadratic forms over the rational numbers. The Witt index of a rational quadratic form is explicitly computed. When combined with a recent adjustment in the Haase invariants, this gives a complete set of invariants for rational quadratic forms, a set which can be computed and which respects all of the standard natural operations (including the tensor product) for quadratic forms. The overall approach does not use (at least explicitly) anyp-adic methods, but it does give the Witt ring of thep-adics as well as the Witt ring of the rationals. 相似文献
9.
David Fried 《Journal of Number Theory》2005,110(1):44-74
Hurwitz developed a reduction theory for real binary quadratic forms of positive discriminant based on least-remainder continued fractions. For each quadratic imaginary field k, we develop a similar theory for complex binary quadratic forms of nonzero discriminant. This uses a Markov partition for the geodesic flow over the quotient of hyperbolic 3-space by the Bianchi group Bk. When k has a Euclidean algorithm, our theory is based on least-remainder continued fractions. 相似文献
10.
Martin ech Dominik Lachman Josef Svoboda Magdalna Tinkov Kristýna Zemkov 《Mathematische Nachrichten》2019,292(3):540-555
The aim of this article is to study (additively) indecomposable algebraic integers of biquadratic number fields K and universal totally positive quadratic forms with coefficients in . There are given sufficient conditions for an indecomposable element of a quadratic subfield to remain indecomposable in the biquadratic number field K. Furthermore, estimates are proven which enable algorithmization of the method of escalation over K. These are used to prove, over two particular biquadratic number fields and , a lower bound on the number of variables of a universal quadratic forms. 相似文献
11.
Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear forms without any symmetry property. The present paper will establish a Witt cancellation result, an analogue of Springer’s theorem, as well as some local–global and finiteness results in this context. 相似文献
12.
Karim Johannes Becher 《Mathematische Zeitschrift》2006,252(1):91-102
In this article weakly isotropic quadratic forms over a (formally) real field are studied. Conditions on the field are given
which imply that every weakly isotropic form over that field has a weakly isotropic subform of small dimension. Fields over
which every quadratic form can be decomposed into an orthogonal sum of a strongly anisotropic form and a torsion form are
characterized in different ways. 相似文献
13.
In this paper, we give parametric families of both real and complex quadratic number fields whose class group has 3-rank at least 2. As a consequence, we obtain that for all large positive real numbers x, the number of both real and complex quadratic fields whose class group has 3-rank at least 2 and absolute value of the discriminant ?x is >cx1/3, where c is some positive constant. 相似文献
14.
A.‐H. Nokhodkar 《Mathematische Nachrichten》2019,292(10):2294-2299
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined result is also obtained for hermitian (resp. skew hermitian) forms over a quaternion algebra with symplectic (resp. orthogonal) involution. 相似文献
15.
The aim of this paper is to prove some results concerning the norm theorem for semisingular quadratic forms, i.e., those which are neither nonsingular nor totally singular. More precisely, we will give necessary conditions in order that an irreducible polynomial, possibly in more than one variable, is a norm ofa semisingular quadratic form, and we prove that our conditions are sufficient if the polynomial is given by a quadratic form which represents 1. As a consequence, we extend the Cassels-Pflster subform theorem to the case of semisingular quadratic forms. 相似文献
16.
We will complete the list of universal binary Hermitian forms over imaginary quadratic fields by investigating three Hermitian forms missed by previous researchers.
17.
LiChao ZhouMin 《高校应用数学学报(英文版)》2004,19(1):9-16
Based on the theory of exponential sums and quadratic forms over finite field, the crosscorrelation function values between two maximal linear recursive sequences are determined under some conditions. 相似文献
18.
We proved some results on the dispersion of the real quadratic irrational numbers, and use LEO 386/25 to compute some numerical results for discriminant <200 (see the attached Table A).The project was supported by a grant from NNSF of P.R. China. 相似文献
19.
Zhu Fuzu 《数学年刊B辑(英文版)》1994,15(3):349-360
CONSTRUCTIONOFINDECOMPOSABLEDEFINITEHERMITIANFORMS¥ZHUFUZU(DepartmelltofMathematics,EastChinaNormalUniversitytShanghai200062,... 相似文献
20.
Vincent Astier 《Indagationes Mathematicae》2008,19(3):349-358
The Bröcker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the Henselizations and isotropy over the real closures of that field. A Hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of Pythagorean index at most two, and algebras over SAP and ED fields. 相似文献