Higher Semiadditivity in Transchromatic Homotopy Theory
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866917827062005760 |
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| author | Ben-Moshe, Shay |
| author_facet | Ben-Moshe, Shay |
| contents | We study the compatibility of higher semiadditivity across different chromatic heights. We prove that the categorified transchromatic character map assembles into a parameterized semiadditive functor, showing that it is higher semiadditive up to a free loop shift. By decategorification, this implies that the transchromatic character map is compatible with integration maps, generalizing the well-known formula for the character of an induced representation. Through a further decategorification process, we compute the higher semiadditive cardinalities of $π$-finite spaces at Lubin-Tate spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00968 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Semiadditivity in Transchromatic Homotopy Theory Ben-Moshe, Shay Algebraic Topology We study the compatibility of higher semiadditivity across different chromatic heights. We prove that the categorified transchromatic character map assembles into a parameterized semiadditive functor, showing that it is higher semiadditive up to a free loop shift. By decategorification, this implies that the transchromatic character map is compatible with integration maps, generalizing the well-known formula for the character of an induced representation. Through a further decategorification process, we compute the higher semiadditive cardinalities of $π$-finite spaces at Lubin-Tate spectra. |
| title | Higher Semiadditivity in Transchromatic Homotopy Theory |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2411.00968 |