arXiv math/05095942005-09-26math.KTmath.AT

From algebraic K-theory to hermitian K-theory

Max Karoubi

备注：: 6 pages, to be published in Comptes Rendus Acad. Sci. Paris, see also http://www.math.jussieu.fr/~karoubi/

英文摘要：

We introduce a new morphism between algebraic and hermitian K-theory. The topological analog is the Adams operation in real K-theory. From this morphism, we deduce a lower bound for the higher algebraic K-theory of a ring A in terms of the classical Witt group of the ring A tensored by its opposite ring.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

A Transfer morphism for Hermitian K-theory of schemes with involution

In this paper, we consider the Hermitian $K$-theory of schemes with involution, for which we construct a transfer morphism and prove a version of the dévissage theorem. This theorem is then used to compute the Hermitian $K$-theory of $\mathbb{P}^1$ with involution given by $[X:Y] \mapsto [Y:X]$. We also prove the $C_2$-equivariant $\A^1$-invariance of Hermitian $K$-theory, which confirms the representability of Hermitian $K$-theory in the $C_2$-equivariant motivic homotopy category of Heller, Krishna and \{O}stvær \cite{HKO14}.

2019-10-14math.KT

On the relation of symplectic algebraic cobordism to hermitian K-theory

We reconstruct hermitian K-theory via algebraic symplectic cobordism. In the motivic stable homotopy category SH(S) there is a unique morphism g : MSp -> BO of commutative ring T- spectra which sends the Thom class th^{MSp} to the Thom class th^{BO}. We show that the induced morphism of bigraded cohomology theories MSp^{*,*} -> BO^{*,*} is isomorphic to the morphism of bigraded cohomology theories obtained by applying to MSp^{*,*} the "change of (simply graded) coefficients rings" MSp^{4*,2*} -> BO^{4*,2*}. This is an algebraic version of the theorem of Conner and Floyd reconstructing real K-t…

2018-03-12math.AGmath.KT

二阶循环群的非常有效代数 K-理论与 Hermitian K-理论

Very effective algebraic and hermitian K-theory of the cyclic group of order two

University of Kentucky（肯塔基大学）；James Madison University（詹姆斯麦迪逊大学）；Duke University（杜克大学）；University of Virginia（弗吉尼亚大学）；University of Pennsylvania（宾夕法尼亚大学）

本文针对代数闭域、实数域和有限域，计算二阶循环群几何分类空间的 $2$-完备整动机同调、有效代数 K-理论与非常有效 Hermitian K-理论。

2026-09-24math.ATmath.KT

A chain morphism for Adams operations on rational algebraic K-theory

For any regular noetherian scheme X and every k>0, we define a chain morphism between two chain complexes whose homology with rational coefficients is isomorphic to the algebraic K-groups of X tensored by the field of rational numbers. It is shown that these morphisms induce in homology the Adams operations defined by Gillet and Soule or the ones defined by Grayson.

2009-04-02math.AGmath.KT

Hermitian K-theory of the integers

The 2-primary torsion of the higher algebraic K-theory of the integers has been computed by Rognes and Weibel. In this paper we prove analogous results for the Hermitian K-theory of the integers with 2 inverted (denoted by Z'). We also prove in this case the analog of the Lichtenbaum conjecture for the hermitian K-theory of Z' : the homotopy fixed point set of a suitable Z/2 action on the classifying space of the algebraic K-theory of Z' is the hermitian K-theory of Z' after 2-adic completion.

2005-09-18math.ATmath.KT

Deformation theory of dialgebra morphisms

An algebraic deformation theory of dialgebra morphisms is obtained.

2006-04-18math.KTmath.RA

更多相关论文收起更多论文

Hermitian lattices and bounds in K-theory of algebraic integers

Elaborating on a method of Soulé, and using better estimates for the geometry of hermitian lattices, we improve the upper bounds for the torsion part of the K-theory of the rings of integers of number fields.

2015-05-21math.KTmath.NT

Algebraic and Hermitian K-theory of K-rings

The main purpose of the present article is to establish the real case of "Karoubi's conjecture" in algebraic K-theory. The complex case was proved in 1990-91 by the second author and Andrei Suslin. Compared to the case of complex algebras, the real case poses additional difficulties. This is due to the fact that topological K-theory of real Banach algebras has period 8 instead of 2. The method we employ to overcome these difficulties can be used for complex algebras, and provides some simplifications to the original proofs. We also establish a natural analog of "Karoubi's conjecture" in Hermit…

2013-10-15math.KT

Periodicity of hermitian K-groups

Bott periodicity for the unitary, orthogonal and symplectic groups is fundamental to topological K-theory. Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients similar periodicity results are consequences of the Milnor and Bloch-Kato conjectures, affirmed by Voevodsky, Rost and others. More generally, we prove that periodicity of the algebraic K-groups for any ring implies periodicity for its hermitian K-groups, analogous to orthogonal and symplectic topological K-theory. The proofs use in an essential way higher KSC theories extending those of Anderson an…

2011-01-11math.KT

On the relation of special linear algebraic cobordism to Witt groups

We reconstruct derived Witt groups via special linear algebraic cobordism. There is a morphism of ring cohomology theories which sends the canonical Thom class in special linear cobordism to the Thom class in the derived Witt groups. We show that for every smooth variety X this morphism induces an isomorphism between MSL^{*,*}(X)[h^{-1}] with the "extended" coefficient ring MSL^{4*,2*}(pt) -> W^{2*}(pt) and Laurent polynomial ring over the derived Witt groups W^*(X), where h is the stable Hopf map. This result is an analogue of the result by Panin and Walter reconstructing hermitian K-theory u…

2015-10-23math.AGmath.KT