Download this article
 Download this article For screen
For printing
Recent Issues
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2379-1691 (online)
ISSN 2379-1683 (print)
 
Author index
To appear
 
Other MSP journals
$\mathbb{A}^1$-invariance of localizing invariants

Vladimir Sosnilo

Vol. 9 (2024), No. 1, 89–118
Abstract

Weibel proved that p-inverted K-theory is 𝔸1-invariant on 𝔽p-schemes and K-theory with p-coefficients is 𝔸1-invariant on [1 p]-schemes. We extend this result to all finitary localizing invariants of small stable -categories. Along the way we study the Frobenius and Verschiebung endofunctors defined by Tabuada and provide a categorical version of Stienstra’s projection formula.

Keywords
noncommutative motives, localizing invariants, $\mathbb{A}^1$-invariance, Witt vectors
Mathematical Subject Classification
Primary: 13F35, 14F42, 18F25
Milestones
Received: 7 January 2023
Revised: 19 February 2024
Accepted: 3 March 2024
Published: 25 May 2024
Authors
Vladimir Sosnilo
Faculty of Mathematics
Universität Regensburg
Regensburg
Germany