Dévissage Hermitian Theory
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913477111578624 |
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| author | Mandal, Satya |
| author_facet | Mandal, Satya |
| contents | We prove Dévissage theorems for Hermitian $K$ Theory (or $GW$ theory), analogous to Quillen's Dévissage theorem for $K$-theory. For abelian categories ${\mathscr A}:=({\mathscr A}, ^{\vee}, \varpi)$ with duality, and appropriate abelian subcategories ${\mathscr B}\subseteq {\mathscr A}$, we prove Dévissage theorems for ${\bf GW}$ spaces, $G{\mathcal W}$-spectra and ${\mathbb G}W$ bispectra. As a consequence, for regular local rings $R$ with $1/2\in R$, we compute the ${\mathbb G}W$ groups ${\mathbb G}W^{[n]}_k(Spec{R})$ forall $k, n\in {\mathbb Z}$, where $n$ represent the translation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09633 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dévissage Hermitian Theory Mandal, Satya K-Theory and Homology Algebraic Geometry We prove Dévissage theorems for Hermitian $K$ Theory (or $GW$ theory), analogous to Quillen's Dévissage theorem for $K$-theory. For abelian categories ${\mathscr A}:=({\mathscr A}, ^{\vee}, \varpi)$ with duality, and appropriate abelian subcategories ${\mathscr B}\subseteq {\mathscr A}$, we prove Dévissage theorems for ${\bf GW}$ spaces, $G{\mathcal W}$-spectra and ${\mathbb G}W$ bispectra. As a consequence, for regular local rings $R$ with $1/2\in R$, we compute the ${\mathbb G}W$ groups ${\mathbb G}W^{[n]}_k(Spec{R})$ forall $k, n\in {\mathbb Z}$, where $n$ represent the translation. |
| title | Dévissage Hermitian Theory |
| topic | K-Theory and Homology Algebraic Geometry |
| url | https://arxiv.org/abs/2408.09633 |