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arXiv · 2504.19078

Arithmetic field theory via pro-p duality groups

Nadav Gropper·Oren Ben-Bassat
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Abstract

Using the theory of pro-p groups and relative Poincar\'{e} 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.

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Nadav Gropper, Oren Ben-Bassat. 2025-04-27. Arithmetic field theory via pro-p duality groups. https://doi.org/0.1007/s11005-026-02058-8

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