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Author

H.-G Quebbemann

Bio: H.-G Quebbemann is an academic researcher from University of Münster. The author has contributed to research in topics: Theta function & Grothendieck group. The author has an hindex of 2, co-authored 2 publications receiving 131 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors give a general foundation for the theory of quadratic and hermitian forms over rings with involution, and show how to solve a number of important classification problems of linear algebra.

125 citations

Journal ArticleDOI
TL;DR: In this article, a modular hermitian lattice with an extremal theta-function was constructed in C 2n for all n R 4n for n = 1, 4, and 8.

15 citations


Cited by
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Journal ArticleDOI
TL;DR: Using invariant theory, a basis is given for the space of invariants to which belongs the three variables weight enumerator of a self-dual code, and a general bound for the weight of such codes is derived.

172 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that an anisotropic quadratic form over a field K is also isomorphic over any odd degree extension of K. If the characteristic of K is not 2, then the canonical map of Galois cohomology sets.
Abstract: Introduction. Let K be a field. Springer has proved that an anisotropic quadratic form over K is also anisotropic over any odd degree extension of K (see [31], [14]). If the characteristic of K is not 2, this implies that two nonsingular quadratic forms that become isomorphic over an extension of odd degree of K are already isomorphic over K (see [31]). In [27], Serre reformulated the latter Statement äs follows: if O is an orthogonal group over K, then the canonical map of Galois cohomology sets

134 citations

Journal ArticleDOI
TL;DR: In this paper, a spectral sequence whose non-zero E 1 -terms are the Witt groups of the residue fields of a regular scheme X, arranged in Gersten-Witt complexes, was constructed.
Abstract: A spectral sequence is constructed whose non-zero E 1 -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.

118 citations

Journal ArticleDOI
TL;DR: The theory of higher Grothendieck-Witt groups, alias algebraic hermitian K-theory, of symmetric bilinear forms in exact categories was studied in this article.
Abstract: We study the theory of higher Grothendieck-Witt groups, alias algebraic hermitian K-theory, of symmetric bilinear forms in exact categories, and prove additivity, cofinality, devissage and localization theorems – preparing the ground for the theory of higher Grothendieck-Witt groups of schemes as developed in [Sch08a] and [Sch08b]. No assumption on the characteristic is being made.

96 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that an n -dimensional unimodular lattice has minimal norm at most 2[ n /24]-2 unless n = 23 when the bound must be increased by 1.

90 citations