The connecting homomorphism for Hermitian $K$-theory
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913249512914944 |
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| author | Huang, Tao Xie, Heng |
| author_facet | Huang, Tao Xie, Heng |
| contents | We provide a geometric interpretation for the connecting homomorphism in the localization sequence of Hermitian $K$-theory. As an application, we compute the Hermitian $K$-theory of projective bundles and Grassmannians in the regular case. We provide an explicit basis for Hermitian $K$-theory of Grassmannians, which is indexed by even Young diagrams together with another special class of Young diagrams, that we call $\textit{buffalo-check}$ Young diagrams. To achieve this, we develop pushforwards and pullbacks in Hermitian $K$-theory using Grothendieck's residue complexes, and we establish fundamental theorems for those pushforwards and pullbacks, including base change, projection, and excess intersection formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_02318 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The connecting homomorphism for Hermitian $K$-theory Huang, Tao Xie, Heng K-Theory and Homology Algebraic Geometry 19G38, 11E81, and 14M15 We provide a geometric interpretation for the connecting homomorphism in the localization sequence of Hermitian $K$-theory. As an application, we compute the Hermitian $K$-theory of projective bundles and Grassmannians in the regular case. We provide an explicit basis for Hermitian $K$-theory of Grassmannians, which is indexed by even Young diagrams together with another special class of Young diagrams, that we call $\textit{buffalo-check}$ Young diagrams. To achieve this, we develop pushforwards and pullbacks in Hermitian $K$-theory using Grothendieck's residue complexes, and we establish fundamental theorems for those pushforwards and pullbacks, including base change, projection, and excess intersection formulas. |
| title | The connecting homomorphism for Hermitian $K$-theory |
| topic | K-Theory and Homology Algebraic Geometry 19G38, 11E81, and 14M15 |
| url | https://arxiv.org/abs/2311.02318 |