3 papers
math.NT2024
Ultra-Galois theory and an analogue of the Kronecker--Weber theorem for rational function fields over ultra-finite fields
Dong Quan Ngoc Nguyen
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 $\mathbb{F}…
math.NT2023
Local symbols and a first-order definition of the polynomial ring over an ultra-finite field in its fraction field
Dong Quan Ngoc Nguyen
In this paper, we prove the existence of a first-order definition of the polynomial ring over a nonprincipal ultraproduct of finite fields of unbounded cardinalities in its fractio…
math.NT2023
Higher reciprocity law and An analogue of the Grunwald--Wang theorem for the ring of polynomials over an ultra-finite field
Dong Quan Ngoc Nguyen
In this paper, we establish an explicit higher reciprocity law for the polynomial ring over a nonprincipal ultraproduct of finite fields. Such an ultraproduct can be taken over the…