AbstractLet q be a power of a prime number p. Let k=Fq(t) be the rational function field with constant field Fq. Let K=k(α) be an Artin–Schreier extension of k. In this paper, we explicitly describe the ambiguous ideal classes and the genus field of K. Using these results, we study the p-part of the ideal class group of the integral closure of Fq[t] in K. We also give an analogue of the Rédei–Reichardt formula for K
Let A=\mathbb{F}_{q}[T] be the polynomial ring in the variable T and K=\mathbb{F}_{q}(T) the...
Let F be a totally real number field of degree n, and let H be a finite abelian extension of F. Let ...
AbstractWe give existence and characterization results for some Artin–Schreier type function fields ...
AbstractLet q be a power of a prime number p. Let k=Fq(t) be the rational function field with consta...
AbstractEmil Artin studied quadratic extensions of k(x) where k is a prime field of odd characterist...
AbstractLet F be a finite geometric separable extension of the rational function field Fq(T). Let E ...
International audienceIn this note we develop an approach to genus theory for a Galois extension L/K...
B. Gross has formulated a conjectural generalization of the class number formula. Suppose $L/K$ is a...
AbstractThe aim of this note is to generalize the Principal Ideal Theorem to the genus field of an a...
International audienceIn this note we develop an approach to genus theory for a Galois extension L/K...
AbstractIn this paper, we determine all finite separable imaginary extensions K/Fq(x) whose maximal ...
For any prime number $p$, we study local triviality of the ideal class group of the ${\boldsymbol Z}...
Let K/Fq be an algebraic function field with full constant field Fq and genus g. Then the divisor cl...
Let A=\mathbb{F}_{q}[T] be the polynomial ring in the variable T and K=\mathbb{F}_{q}(T) the...
Let k be an algebraically closed field, G(u) a polynomial in the indeterminate u. Let k(u) be the ra...
Let A=\mathbb{F}_{q}[T] be the polynomial ring in the variable T and K=\mathbb{F}_{q}(T) the...
Let F be a totally real number field of degree n, and let H be a finite abelian extension of F. Let ...
AbstractWe give existence and characterization results for some Artin–Schreier type function fields ...
AbstractLet q be a power of a prime number p. Let k=Fq(t) be the rational function field with consta...
AbstractEmil Artin studied quadratic extensions of k(x) where k is a prime field of odd characterist...
AbstractLet F be a finite geometric separable extension of the rational function field Fq(T). Let E ...
International audienceIn this note we develop an approach to genus theory for a Galois extension L/K...
B. Gross has formulated a conjectural generalization of the class number formula. Suppose $L/K$ is a...
AbstractThe aim of this note is to generalize the Principal Ideal Theorem to the genus field of an a...
International audienceIn this note we develop an approach to genus theory for a Galois extension L/K...
AbstractIn this paper, we determine all finite separable imaginary extensions K/Fq(x) whose maximal ...
For any prime number $p$, we study local triviality of the ideal class group of the ${\boldsymbol Z}...
Let K/Fq be an algebraic function field with full constant field Fq and genus g. Then the divisor cl...
Let A=\mathbb{F}_{q}[T] be the polynomial ring in the variable T and K=\mathbb{F}_{q}(T) the...
Let k be an algebraically closed field, G(u) a polynomial in the indeterminate u. Let k(u) be the ra...
Let A=\mathbb{F}_{q}[T] be the polynomial ring in the variable T and K=\mathbb{F}_{q}(T) the...
Let F be a totally real number field of degree n, and let H be a finite abelian extension of F. Let ...
AbstractWe give existence and characterization results for some Artin–Schreier type function fields ...
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