Arithmetic field theory via pro-p duality groups
Abstract
Abstract 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.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Advanced Algebra and Geometry
Geometric and Algebraic Topology
Publication details
- Journal / source
- Letters in Mathematical Physics
- Volume
- 116
- Issue
- 2
- Publication date
- 4 March 2026
- Language
- EN