Algebraic K-theory of quadratic forms (Q1113995)

scientific article; zbMATH DE number 4083881

Language	Label	Description	Also known as
English	Algebraic K-theory of quadratic forms	scientific article; zbMATH DE number 4083881

Statements

instance of

scholarly article

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title

Algebraic K-theory of quadratic forms (English)

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author

Yu. P. Solovyev

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published in

Journal of Soviet Mathematics

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publication date

1989

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review text

See the review in Zbl 0631.18011.

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zbMATH Keywords

applications to algebraic topology

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survey

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algebraic K-theory of quadratic forms over rings

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On the normal subgroups of the orthogonal group over a ring with involution.

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ON UNIVERSALITY FOR GEU UNITARY RINGS

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Witt classes of integral representations of an Abelian $p$-group

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Q4175744

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Surgery with coefficients

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Q4169437

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Computation of the surgery obstruction groups $L_{4k}(1;\mathbb{Z}_p)$

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Cohomologische Invarianten quadratischer Formen

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Quadratic forms over semilocal rings

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Q4115834

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The computation of surgery groups of odd torsion groups

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Odd dimension surgery groups of odd torsion groups vanish

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Grothendieck Groups of Modules and Forms Over Commutative Orders

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The computation of even dimension surgery groups of odd torsion groups

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Arf's theorem for trace Noetherian and other rings

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K-Theory of Forms. (AM-98)

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The computation of odd dimensional projective surgery groups of finite groups

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Grothendieck and Witt groups of orders and finite groups

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Q4053793

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Clifford Algebras and Spinor Norms Over a Commutative Ring

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L$_3$ of finite Abelian groups

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Some hybrid symplectic group phenomena

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The reduced theory of quadratic forms

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Q3704618

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A splitting theorem for manifolds and surgery groups

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On connected sums of manifolds

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Unitary nilpotent groups and Hermitian $K$-theory. I

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The codimension two placement problem and homology equivalent manifolds

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ON THE WITT GROUP OF A 2-ADIC GROUP RING

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Wu invariants of Hermitian forms

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Q4195115

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Q3903154

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Some exact sequences in the theory of Hermitian forms

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L-theory and the Arf invariant

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Q4195623

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Q3907640

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Linking numbers and surgery

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Characterizing reduced Witt rings of fields

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Characterizing reduced Witt rings. II

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Q4097457

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Q4075643

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Bilinear and quadratic forms on torsion modules

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Quadratic forms under algebraic extensions

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Q3051117

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Manifolds with π 1 = G x α T

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Rational L-groups of Bieberbach groups

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On Novikov's conjecture for non-positively curved manifolds. I

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ON THE <i>K</i>-THEORY OF UNIMODULAR FORMS OVER RINGS OF ALGEBRAIC INTEGERS

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Forms over rings with involution

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A remark on the quadratic analogue of the Quillen-Suslin theorem.

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Hermitian forms and higher algebraic 𝐾-theory

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Q3969588

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Q3903155

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The surgery obstruction groups for finite 2-groups

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Homological surgery

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On Odd Dimensional Surgery with Finite Fundamental Group

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On the Witt ring and some arithmetical invariants of quadratic forms

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Hermitesche und orthogonale Operatoren über kommutativen Ringen

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Q5628909

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Q5631789

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Localisation de formes quadratiques $I$

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Q4405059

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Localisation de formes quadratiques. II

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Q4108440

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Le théorème fondamental de la K-théorie hermitienne

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Théorie de Quillen et homologie du groupe orthogonal

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Q5618464

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The Witt ring of a full ring

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Specialization of quadratic and symmetric, bilinear forms, and a norm theorem

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Generic Splitting of Quadratic Forms, I

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Q3934471

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Q3880903

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Q4179116

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Modules and Quadratic Forms over Polynomial Algebras

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Computations of Witt groups of finite groups

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Q4747251

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Q5675788

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Q4080436

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Computation of Wall groups

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Frobenius algebras and hermitian forms

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Quadratische Formen über Körpern

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The prime ideals of Witt rings

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Q5683974

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Some Local-Global Principles for Formally Real Fields

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Some relative notions in the theory of Hermitian forms

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The orthogonal group over a full ring

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Forms over semisimple algebras with involution

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Q3876003

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The geometric realization of a semi-simplicial complex

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A product formula for surgery obstructions

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Induction theorems for groups of homotopy manifold structures

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Q4179114

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A splitting theorem for quadratic forms

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Local surgery and applications to the theory of quadratic forms

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Q4143895

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Q4135704

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Local surgery and the exact sequence of a localization for Wall groups

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An invariant determining the Witt class of a unitary transformation over a semisimple ring

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Q4742858

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Failure of a quadratic analogue of Serre’s conjecture

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Failure of a Quadratic Analogue of Serre's Conjecture

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Quadratic Forms Over Polynomial Rings Over Dedekind Domains

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Quadratic forms over polynomial extensions of rings of dimension one

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Surgery with coefficients in a field

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𝐵_{(𝑇𝑂𝑃_{𝑛})^{∼}} and the surgery obstruction

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Algebraic <i>L</i> -Theory, I: Foundations

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Q4405330

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Algebraic $L$-theory. IV: Polynomial extension rings

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On the algebraic $L$-theory of semisimple rings

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Q3208860

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The Algebraic Theory of Surgery I. Foundations

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The Algebraic Theory of Surgery II. Applications to Topology

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Q3924852

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Witt's theorem for noncommutative semilocal rings

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Groupes de Witt d'un corps de caractéristique 2.

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Induction theorems and the structure of the Witt group

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Involutions on orders. I.

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Classifying spaces and spectral sequences

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Wall’s surgery obstruction groups for 𝑍×𝐺, for suitable groups 𝐺

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Wall's surgery obstruction groups for GxZ

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Product formulas for $L_n \left( \pi \right)$

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Q4778063

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On the structure of the unitary Steinberg group

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Surgery on compact manifolds: The bounded even dimensional case

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Unitary Whitehead group of cyclic groups

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Unitary Whitehead group of cyclic groups

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Homology surgery theory and perfect groups

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Frobenius reciprocity of Hermitian forms

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Zur Theorie quadratischer Formen über Körpern der Charakteristik 2.

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Some Witt Cancellation Theorems

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Delooping classifying spaces in algebraic K-theory

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Surgery of non-simply-connected manifolds

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Q5594673

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Q5624419

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Q5611913

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On the classification of Hermitian forms. II: Semisimple rings

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On the classification of Hermitian forms. III: Complete semilocal rings

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Some 𝐿 groups of finite groups

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On the commutator subgroups of certain unitary groups

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On the classification of Hermitian forms. IV: Adele rings

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On the classification of Hermitian forms. V: Global rings

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Classification of Hermitian forms. VI: Group rings

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Surgery and bordism invariants

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Q5763684

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Q4145888

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Identifiers

zbMATH Open document ID

0663.18007

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DOI

10.1007/BF01676869

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:1113995