Arithmetic field theory via pro-p duality groups

Key Points

• The research aims to define a cobordism category and classify topological quantum field theories relevant to arithmetic topology.
• Utilized pro-p groups and relative Poincaré duality to define a cobordism category.
• Classified two-dimensional topological quantum field theories on the created cobordism categories.
• Investigated Frobenius algebras tied to automorphisms of p-adic integers.
• Focused on arithmetic Dijkgraff–Witten theory for finite gauge p-groups.
• Successfully classified topological quantum field theories on the defined cobordism categories.
• Derived formulae for counting Galois extensions of local p-adic fields with specific Galois groups.