Hermitian k-theory

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August undefined, 2024

Witryna1 lip 2024 · Within the framework of dg categories with weak equivalences and duality that have uniquely 2-divisible mapping complexes, we show that higher … Witryna1 kwi 2024 · This theorem is then used to compute the Hermitian K-theory of P 1 with involution given by [X: Y] ↦ [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 Østvær [14].

Hermitian K-theory of exact categories - Warwick

WitrynaHERMITIAN K-THEORY FOR STABLE ∞-CATEGORIES I: FOUNDATIONS BAPTISTE CALMÈS, EMANUELE DOTTO, YONATAN HARPAZ, FABIAN HEBESTREIT, MARKUS LAND, KRISTIAN MOI, DENIS NARDIN, THOMAS NIKOLAUS, AND WOLFGANG STEIMLE To Andrew Ranicki. ABSTRACT. This paper is the ﬁrst in a series in which … Witryna29 mar 2024 · Abstract We show that the hermitian K-theory space of a commutative ring R can be identified, up to 𝐀 1 {\mathbf{A}^{1}} -homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-algebras, i.e., finite locally free R-algebras with trivialized dualizing sheaf. We deduce that hermitian K-theory is universal … gst new home rebate application

MARCO SCHLICHTING arXiv:1209.0848v3 [math.KT] 7 Sep 2016

WitrynaSome hermitian K-groups via geometric topology HTML articles powered by AMS MathViewer by Manuel Krannich and Alexander Kupers PDF Proc. Amer. Math. Soc. 149 (2024), 2745-2752 Request permission Abstract: We compute the first two symplectic quadratic K-theory groups of the integers, or equivalently, the first two stable … Witryna15 wrz 2024 · Download a PDF of the paper titled Hermitian K-theory for stable $\infty$-categories II: Cobordism categories and additivity, by Baptiste Calm\`es and 7 other authors. Download PDF Abstract: We define Grothendieck-Witt spectra in the setting of Poincaré $\infty$-categories and show that they fit into an extension with a K- and an … Witryna13 lis 2009 · We study the theory of higher Grothendieck-Witt groups, alias algebraic hermitian K -theory, of symmetric bilinear forms in exact categories, and prove … gst new act

HERMITIAN K-THEORY. THE THEORY OF CHARACTERISTIC …

arXiv:2009.07223v2 [math.KT] 26 Mar 2024 - University of Rochester

Witryna1 sty 2006 · Cite this paper. Bass, M. (1973). Unitary algegraic K-theory. In: Bass, H. (eds) Hermitian K-Theory and Geometric Applications. Witryna16 maj 2011 · Bott periodicity for the unitary and symplectic groups is fundamental to topological K-theory.Analogous to unitary topological K-theory, for algebraic K-groups with finite coefficients, similar results are consequences of the Milnor and Bloch-Kato conjectures, affirmed by Voevodsky, Rost and others.More generally, we prove that … financial information act guidance packageWitryna7 kwi 2024 · The Witt group of skew hermitian forms over a division algebra with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of with values in a suitable line bundle. In the special case where is a quaternion algebra we extend previous work by … financial information for heirs

"Witryna6 lis 2009 · We prove localization and Zariski-Mayer-Vietoris for higher Gro-thendieck-Witt groups, alias hermitian K-groups, of schemes admitting an ample family of line-bundles. No assumption on the characteristic is needed, and our schemes can be singular. Along the way, we prove Additivity, Fibration and Approximation theorems … " - Hermitian k-theory

Hermitian k-theory

An Artin-Schreier-type theory for signatures of hermitian forms …

Witryna7 gru 2014 · The purpose of this article is to prove a result analogous to for the theory of higher Grothendieck–Witt groups, a.k.a. algebraic hermitian $K$-theory , extended to schemes in . Our result has already been used in the work of [ 1 , 18 ] and opens the door to a classification of unstable operations in Grothendieck–Witt theory as done in ... Witryna2 paź 2024 · motivic homotopy theory, slice filtration, motivic cohomology, algebraic K-theory, Hermitian K-theory, higher Witt-theory, quadratic forms over rings of integers, special values of Dedekind ζ-functions of number fields. 2010 Mathematics Subject Classification 11R42, 14F42, 19E15, 19F27

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Witryna4 gru 2024 · We argue that the very effective cover of hermitian $K$-theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the ... Witryna15 wrz 2024 · Download a PDF of the paper titled Hermitian K-theory for stable $\infty$-categories II: Cobordism categories and additivity, by Baptiste Calm\`es and 7 other …

WitrynaWe argue that the very effective cover of hermitian K-theory in the sense of motivic homotopy theory is a convenient algebro-geometric generalization of the connective real topological K-theory spectrum. This means the very effective cover acquires the correct Betti realization, its motivic cohomology has the desired structure as a module over … Witryna30 kwi 1976 · Lomonosov Moscow State University. This paper gives a survey of results on Hermitian K-theory over the last ten years. The main emphasis is on the …

Witryna23 lip 2004 · The homotopy limit problem for Hermitian K-theory, equivariant motivic homotopy theory and motivic Real cobordism. Advances in Mathematics, Vol. 228, Issue. 1, p. 434. CrossRef; Google Scholar; Röndigs, Oliver and Østvær, Paul 2016. Slices of hermitian K–theory and Milnor’s conjecture on quadratic forms. Geometry … Witryna11 cze 2024 · The theory provides a universal understanding of non-Hermitian topological phenomena such as the unidirectional transport in one dimension and the chiral magnetic skin effect in three dimensions and systematically predicts new physics by revealing transport phenomena and skin effects in two dimensions induced by a …

WitrynaWe advance the understanding of K–theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K–groups and Witt groups. By an explicit …

WitrynaThis study outlines the necessary and sufficient criteria for swarm stability asymptotically, meaning consensus in a class of fractional-order multi-agent systems (FOMAS) with interval uncertainties for both fractional orders 0 < α < 1 and 1 < α < 2. The constraints are determined by the graph topology, agent dynamics, and … gst new notification 2021WitrynaThursday Seminar Fall 2024 – Hermitian K-theory. The goal of this seminar is to understand the seminal work of Calmés, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus, Steimle on Hermitian -theory. financial information for retiring singlesWitrynaHERMITIAN K-THEORY AND DERIVED EQUIVALENCES 3 with (weak equivalences and) duality is deﬁned to be the Grothendieck-Witt group of the exact category with weak equivalences and duality in the sense of [Sch10b, Deﬁnition 1] of the category Z0Aptr of closed degree zero maps in the pretriangu-lated hull of A. gst new rates 2021WitrynaarXiv.org e-Print archive financial information is presented belowWitryna28 mar 2024 · The non-Hermitian effect is different from parity-time (PT) symmetry, and can be explained by a simple coupled-mode theory with an anti-PT symmetry. The existence of exceptional points and slow-light effect are discussed. This work highlights the potential of loss-free negative-index materials in the study of non-Hermitian optics. financial information for decision makingWitryna1 kwi 2024 · This theorem is then used to compute the Hermitian K-theory of P 1 with involution given by [X: Y] ↦ [Y: X]. We also prove the C 2-equivariant A 1-invariance … financial information of a companyWitryna17 lis 2024 · This paper is the first in a series in which we offer a new framework for hermitian $${\\text {K}}$$ K -theory in the realm of stable $$\\infty $$ ∞ -categories. … financial information of healthcare