On the K-theory of regular coconnective rings
Abstract We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $$\pi _0$$...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2023
|
| Online Access: | https://hdl.handle.net/1721.1/148491 |
| _version_ | 1811074374763020288 |
|---|---|
| author | Burklund, Robert Levy, Ishan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Burklund, Robert Levy, Ishan |
| author_sort | Burklund, Robert |
| collection | MIT |
| description | Abstract
We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its
$$\pi _0$$
π
0
. We prove this as a consequence of a more general devissage result for stable infinity categories. Applications of our result include giving general conditions under which K-theory preserves pushouts, generalizations of
$$\mathbb {A}^n$$
A
n
-invariance of K-theory, and an understanding of the K-theory of categories of unipotent local systems. |
| first_indexed | 2024-09-23T09:48:04Z |
| format | Article |
| id | mit-1721.1/148491 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:48:04Z |
| publishDate | 2023 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1484912024-01-12T19:38:00Z On the K-theory of regular coconnective rings Burklund, Robert Levy, Ishan Massachusetts Institute of Technology. Department of Mathematics Abstract We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $$\pi _0$$ π 0 . We prove this as a consequence of a more general devissage result for stable infinity categories. Applications of our result include giving general conditions under which K-theory preserves pushouts, generalizations of $$\mathbb {A}^n$$ A n -invariance of K-theory, and an understanding of the K-theory of categories of unipotent local systems. 2023-03-13T12:06:46Z 2023-03-13T12:06:46Z 2023-03-08 2023-03-12T04:11:50Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/148491 Selecta Mathematica. 2023 Mar 08;29(2):28 PUBLISHER_CC en https://doi.org/10.1007/s00029-023-00833-2 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Burklund, Robert Levy, Ishan On the K-theory of regular coconnective rings |
| title | On the K-theory of regular coconnective rings |
| title_full | On the K-theory of regular coconnective rings |
| title_fullStr | On the K-theory of regular coconnective rings |
| title_full_unstemmed | On the K-theory of regular coconnective rings |
| title_short | On the K-theory of regular coconnective rings |
| title_sort | on the k theory of regular coconnective rings |
| url | https://hdl.handle.net/1721.1/148491 |
| work_keys_str_mv | AT burklundrobert onthektheoryofregularcoconnectiverings AT levyishan onthektheoryofregularcoconnectiverings |