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Preprint Number 2689
2689. Dong Quan Ngoc Nguyen Ultra-Galois theory and an analogue of the Kronecker--Weber theorem for rational function fields over ultra-finite fields E-mail: Submission date: 4 August 2024 Abstract: In the first part of this paper, we develop a general framework that permits
a comparison between explicit class field theories for a family of rational
function fields 𝔽_s(t) over arbitrary constant fields 𝔽_s
and explicit class field theory for the rational function field
𝔎(t) over the nonprincipal ultraproduct 𝔎 of the
constant fields 𝔽_s. Under an additional assumption that the
constant fields 𝔽_s are perfect procyclic fields, we prove a
correspondence between ramifications of primes P in 𝔎(t) and
ramifications of primes P_s in 𝔽_s(t), where the P_s are primes
in 𝔽_s(t) whose nonprincipal ultraproduct coincides with P. Mathematics Subject Classification: Keywords and phrases: |
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