ALEXANDER VISHIK ALEXANDER.VISHIK@NOTTINGHAM.AC.UK
Professor of Algebra
Operations in connective K-theory
Vishik, Alexander; Merkurjev, Alexander
Authors
Alexander Merkurjev
Abstract
We classify additive operations in connective K-theory with various torsion-free coefficients. We discover that the answer for the integral case requires understanding of the ˆZ case. Moreover, although integral additive operations are topologically generated by Adams operations, these are not reduced to infinite linear combinations of the latter ones. We describe a topological basis for stable operations and relate it to a basis of stable operations in graded K-theory. We classify multiplicative operations in both theories and show that homogeneous additive stable operations with ˆZ-coefficients are topologically generated by stable multiplicative operations. This is not true for integral operations.
Citation
Vishik, A., & Merkurjev, A. (2023). Operations in connective K-theory. Algebra and Number Theory, 17(9), 1595–1636. https://doi.org/10.2140/ant.2023.17.1595
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 4, 2022 |
Online Publication Date | Sep 9, 2023 |
Publication Date | Sep 9, 2023 |
Deposit Date | Dec 21, 2022 |
Publicly Available Date | Sep 9, 2023 |
Journal | Algebra and Number Theory |
Print ISSN | 1937-0652 |
Electronic ISSN | 1944-7833 |
Publisher | Mathematical Sciences Publishers |
Peer Reviewed | Peer Reviewed |
Volume | 17 |
Issue | 9 |
Pages | 1595–1636 |
DOI | https://doi.org/10.2140/ant.2023.17.1595 |
Keywords | Algebra and Number Theory |
Public URL | https://nottingham-repository.worktribe.com/output/14588784 |
Publisher URL | https://msp.org/ant/2023/17-9/p03.xhtml |
Files
CK-ANT-3
(475 Kb)
PDF
You might also like
Symmetric operations for all primes and Steenrod operations in Algebraic Cobordism
(2016)
Journal Article
Algebraic Cobordism as a module over the Lazard ring
(2015)
Journal Article
Stable and unstable operations in algebraic cobordism
(2019)
Journal Article
Motivic equivalence of affine quadrics
(2018)
Journal Article
Affine quadrics and the Picard group of the motivic category
(2019)
Journal Article
Downloadable Citations
About Repository@Nottingham
Administrator e-mail: discovery-access-systems@nottingham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search