Equivariant Algebraic K-Theories
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908641644249088 |
|---|---|
| author | Yau, Donald |
| author_facet | Yau, Donald |
| contents | A cornerstone of algebraic K-theory is the equivalence between the K-theory machines of May, Segal, and Elmendorf and Mandell. Equivariant algebraic K-theory enriches the theory with group actions, making it more powerful and complex. There are a number of equivariant K-theory machines that turn equivariant categorical data into equivariant spectra, the main objects of study in equivariant stable homotopy theory.
This work proves that the following four equivariant K-theory machines are appropriately equivalent: Shimakawa equivariant K-theory; the author's enriched multifunctorial equivariant K-theory; the equivariant K-theory of Guillou, May, Merling, and Osorno; and Schwede global equivariant K-theory. Parts 1 and 2 prove the topological equivalence between Shimakawa and multifunctorial equivariant K-theories. Part 3 proves that their categorical parts are equivalent. Part 4 proves that the equivariant K-theory of Guillou, May, Merling, and Osorno is equivalent to Shimakawa K-theory and Schwede global K-theory for each finite group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Algebraic K-Theories Yau, Donald Algebraic Topology K-Theory and Homology 18M65, 18D20, 19D23, 19L47, 55P43, 55P91 A cornerstone of algebraic K-theory is the equivalence between the K-theory machines of May, Segal, and Elmendorf and Mandell. Equivariant algebraic K-theory enriches the theory with group actions, making it more powerful and complex. There are a number of equivariant K-theory machines that turn equivariant categorical data into equivariant spectra, the main objects of study in equivariant stable homotopy theory. This work proves that the following four equivariant K-theory machines are appropriately equivalent: Shimakawa equivariant K-theory; the author's enriched multifunctorial equivariant K-theory; the equivariant K-theory of Guillou, May, Merling, and Osorno; and Schwede global equivariant K-theory. Parts 1 and 2 prove the topological equivalence between Shimakawa and multifunctorial equivariant K-theories. Part 3 proves that their categorical parts are equivalent. Part 4 proves that the equivariant K-theory of Guillou, May, Merling, and Osorno is equivalent to Shimakawa K-theory and Schwede global K-theory for each finite group. |
| title | Equivariant Algebraic K-Theories |
| topic | Algebraic Topology K-Theory and Homology 18M65, 18D20, 19D23, 19L47, 55P43, 55P91 |
| url | https://arxiv.org/abs/2511.07556 |