Arithmetic field theory via pro-p duality groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917331999916032 |
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| author | Gropper, Nadav Ben-Bassat, Oren |
| author_facet | Gropper, Nadav Ben-Bassat, Oren |
| contents | Using the theory of pro-p groups and relative Poincaré duality, we define a type of cobordism category well suited to arithmetic topology. We completely classify topological quantum field theories on these two-dimensional versions of our cobordism categories. This classification uses Frobenius algebras with extra operations corresponding to automorphisms of the p-adic integers. We look in more detail at the example of arithmetic Dijkgraff--Witten theory for a finite gauge p-group in this setting. This allows us to deduce formulae counting Galois extensions of local p-adic fields whose Galois groups are the given gauge group. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_19078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arithmetic field theory via pro-p duality groups Gropper, Nadav Ben-Bassat, Oren Number Theory Mathematical Physics Algebraic Topology 81T40, 57R90, 57R56, 11S20 Using the theory of pro-p groups and relative Poincaré duality, we define a type of cobordism category well suited to arithmetic topology. We completely classify topological quantum field theories on these two-dimensional versions of our cobordism categories. This classification uses Frobenius algebras with extra operations corresponding to automorphisms of the p-adic integers. We look in more detail at the example of arithmetic Dijkgraff--Witten theory for a finite gauge p-group in this setting. This allows us to deduce formulae counting Galois extensions of local p-adic fields whose Galois groups are the given gauge group. |
| title | Arithmetic field theory via pro-p duality groups |
| topic | Number Theory Mathematical Physics Algebraic Topology 81T40, 57R90, 57R56, 11S20 |
| url | https://arxiv.org/abs/2504.19078 |