Download this article
Download this article For screen
For printing
Recent Issues
Volume 9, Issue 4
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
The universal six-functor formalism

Brad Drew and Martin Gallauer

Vol. 7 (2022), No. 4, 599–649
DOI: 10.2140/akt.2022.7.599
Abstract

We prove that Morel–Voevodsky’s stable 𝔸1-homotopy theory affords the universal coefficient system, giving rise to Grothendieck’s six operations.

Keywords
motivic homotopy theory, $\mathbb A^1$-homotopy, coefficient system, six operations, six-functor formalism
Mathematical Subject Classification
Primary: 14F20, 14F42, 18N60
Milestones
Received: 19 July 2021
Revised: 17 September 2022
Accepted: 30 October 2022
Published: 15 March 2023
Authors
Brad Drew
Albert-Ludwigs-Universität Freiburg
Freiburg
Germany
Martin Gallauer
Max-Planck-Institut für Mathematik
Bonn
Germany