共查询到20条相似文献,搜索用时 31 毫秒
1.
Two fields are Witt equivalent if their Witt rings of symmetric bilinear forms are isomorphic. Witt equivalent fields can be understood to be fields having the same quadratic form theory. The behavior of finite fields, local fields, global fields, as well as function fields of curves defined over Archimedean local fields under Witt equivalence is well understood. Numbers of classes of Witt equivalent fields with finite numbers of square classes are also known in some cases. Witt equivalence of general function fields over global fields was studied in the earlier work [13] by the authors and applied to study Witt equivalence of function fields of curves over global fields. In this paper, we extend these results to local case, i.e. we discuss Witt equivalence of function fields of curves over local fields. As an application, we show that, modulo some additional assumptions, Witt equivalence of two such function fields implies Witt equivalence of underlying local fields. 相似文献
2.
Przemysław Koprowski 《Czechoslovak Mathematical Journal》2007,57(4):1311-1319
We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we
deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a
local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group. 相似文献
3.
Przemysław Koprowski 《Mathematische Zeitschrift》2002,242(2):323-345
We examine the conditions for two algebraic function fields over real closed fields to be Witt equivalent. We show that there
are only two Witt classes of algebraic function fields with a fixed real closed field of constants: real and non-real ones.
The first of them splits further into subclasses corresponding to the tame equivalence. This condition has a natural interpretation
in terms of both: orderings (the associated Harrison isomorphism maps 1-pt fans onto 1-pt fans), and geometry and topology
of associated real curves (the bijection of points is a homeomorphism and these two curves have the same number of semi-algebraically
connected components). Finally, we derive some immediate consequences of those theorems. In particular we describe all the
Witt classes of algebraic function fields of genus 0 and 1 over the fixed real closed field.
Received: 16 February 2000; in final form: 7 December 2000 / Published online: 18 January 2002 相似文献
4.
Kazimierz Szymiczek 《Semigroup Forum》2000,60(2):260-270
For semigroups with divisor theory we introduce an equivalence relation that preserves the p -dimensions of divisor class groups. While the approach has been motivated by the results on Hilbert-symbol equivalence in quadratic form theory over algebraic number fields, it is the purpose of the paper to generalize the setup to semigroups with divisor theory and to simplify the proofs by avoiding any ring- or number-theoretical arguments. 相似文献
5.
6.
Paul Balmer 《K-Theory》2001,23(1):15-30
We establish a Mayer–Vietoris long exact sequence for Witt groups of regular schemes. We also establish homotopy invariance for Witt groups of regular schemes. For this, we introduce Witt groups with supports using triangulated categories. Subsequently, we use these results to prove the Gersten–Witt conjecture for semi-local regular rings of geometric type over infinite fields of characteristic different from two. 相似文献
7.
Manfred Lochter 《Israel Journal of Mathematics》1993,84(1-2):89-96
In [12] and [13] Jack Sonn has introduced and studied a new notion of equivalence for number fields. In this note we show
that “almost all” (cf. [14]) pairs of equivalent number fields are conjugate over ℚ, and we study equivalence classes of fields
of prime degree. 相似文献
8.
Marcus Zibrowius 《Mathematische Zeitschrift》2014,278(1-2):191-227
9.
Przemysław Koprowski 《Mathematica Slovaca》2007,57(5):407-414
We present here two new criteria for existence of a tame Harrison map of two formally real algebraic function fields over
a fixed real closed field of constants. The first criterion (c.f. Theorem 2.5) shows that a square class group isomorphism
is a tame Harrison map if it induces an isomorphism of the coproduct rings of residue Witt rings. The other result (c.f. Proposition
3.5) associates a tame Harrison map to an integral quaternion-symbol equivalence.
相似文献
10.
Complete classification of formally real fields with 8 square classes with respect to the behaviour of quadratic forms is given. Two fields F and K are equivalent with respect to quadratic forms if the quadratic form schemes of the two fields are isomorphic or in other words, if the Witt rings W(F) and W(K) are isomorphic. It is shown here that for formally real fields with 8 square classes there are exactly seven possible quadratic form schemes and for each of the seven schemes a formally real field with 8 square classes and the given scheme is constructed. 相似文献
11.
Jeremy Jacobson 《Journal of Algebra》2012,351(1):254-278
For smooth varieties over finite fields, we prove that the shifted (aka derived) Witt groups of surfaces are finite and the higher Grothendieck–Witt groups (aka Hermitian K-theory) of curves are finitely generated. For more general arithmetic schemes, we give conditional results, for example, finite generation of the motivic cohomology groups implies finite generation of the Grothendieck–Witt groups. 相似文献
12.
This article is concerned with describing certain bilinear forms associated with finite abelian extensions N|K of an algebraic number field K. These abelian trace forms are described up to Witt equivalence, that is, they are described as elements in the Witt ring W(K). When the base field K has exactly one dyadic prime and no real embeddings, it is shown that the Witt class of every abelian trace form over K is a product of Witt classes of five specified types. 相似文献
13.
A. D. Maksimov 《Journal of Mathematical Sciences》2012,183(3):397-406
The paper is devoted to the notion of typical equivalence introduced by B. I. Plotkin. We give some examples of elementarily equivalent objects that are not typically equivalent and show two ways to construct nonisomorphic typically equivalent algebras. We also prove A. I. Maltsev??s theorem on elementary equivalence of linear groups over fields for the case of typical equivalence. 相似文献
14.
I. Dejaiffe J. P. Tignol D. W. Lewis 《Rendiconti del Circolo Matematico di Palermo》1925,49(2):325-342
The notion of Witt equivalence of central simple algebras with involution is introduced. It is shown that the standard invariants, i.e. the discriminant, the signature and the Clifford algebra, depend only on the Witt class of the algebra with involution. For a given filedF the tensor product is used to construct a semigroup\(\tilde S\left( F \right)\) and this semigroup is shown to have properties analogous to the multiplicative properties of the Witt ring of quadratic forms overF. 相似文献
15.
The Witt group of a hyperelliptic curve over a field of characteristic different from two was determined by Parimala and Sujatha. Here, analogous results are obtained for the unramified Witt group in characteristic two using the analogue of Milnor's exact sequence for the Witt group of rational function fields developed earlier by the authors. In the elliptic case, if F is perfect and points of order two are rational, a generator and relation structure for the Witt group is given. 相似文献
16.
Institutional Logics from the Aggregation of Organizational Networks: Operational Procedures for the Analysis of Counted Data 总被引:2,自引:0,他引:2
We address some problems of network aggregation that are central to organizational studies. We show that concepts of network equivalence (including generalizations and special cases of structural equivalence) are relevant to the modeling of the aggregation of social categories in cross-classification tables portraying relations within an organizational field (analogous to one-mode networks). We extend our results to model the dual aggregation of social identities and organizational practices (an example of a two-mode network). We present an algorithm to accomplish such dual aggregation. Within the formal and quantitative framework that we present, we emphasize a unified treatment of (a) aggregation on the basis of structural equivalence (invariance of actors within equivalence sets), (b) the study of variation in relations between structurally equivalent sets, and (c) the close connections between aggregation within organizational networks and multi-dimensional modeling of organizational fields. 相似文献
17.
I. Dejaiffe J. P. Tignol D. W. Lewis 《Rendiconti del Circolo Matematico di Palermo》2000,49(2):325-342
The notion of Witt equivalence of central simple algebras with involution is introduced. It is shown that the standard invariants,
i.e. the discriminant, the signature and the Clifford algebra, depend only on the Witt class of the algebra with involution.
For a given filedF the tensor product is used to construct a semigroup
and this semigroup is shown to have properties analogous to the multiplicative properties of the Witt ring of quadratic forms
overF. 相似文献
18.
Paul Balmer 《Annales Scientifiques de l'école Normale Supérieure》2002,35(1):127-152
A spectral sequence is constructed whose non-zero E1-terms are the Witt groups of the residue fields of a regular scheme X, arranged in Gersten-Witt complexes, and whose limit is the four global Witt groups of X. This has several immediate consequences concerning purity for Witt groups of low-dimensional schemes. We also obtain an easy proof of the Gersten Conjecture in dimension smaller than 5. The Witt groups of punctured spectra of regular local rings are also computed. 相似文献
19.
Larry J. Gerstein 《Linear algebra and its applications》1977,16(3):221-232
Matrix equivalence over principal ideal domains is considered, using the technique of localization from commutative algebra. This device yields short new proofs for a variety of results. (Some of these results were known earlier via the theory of determinantal divisors.) A new algorithm is presented for calculation of the Smith normal form of a matrix, and examples are included. Finally, the natural analogue of the Witt–Grothendieck ring for quadratic forms is considered in the context of matrix equivalence. 相似文献
20.
For fields of characteristic zero, we show that the homotopy category of modules over the motivic ring spectrum representing motivic cohomology is equivalent to Voevodsky's big category of motives. The proof makes use of some highly structured models for motivic stable homotopy theory, motivic Spanier-Whitehead duality, the homotopy theories of motivic functors and of motivic spaces with transfers as introduced from ground up in this paper. Working with rational coefficients, we extend the equivalence for fields of characteristic zero to all perfect fields by employing the techniques of alterations and homotopy purity in motivic homotopy theory. 相似文献