Arithmetic Characterization of Algebraic Number Fields with Small Class Numbers.
On reciprocity equivalence of quadratic number fields
Hilbert-symbol equivalence of global function fields
Witt equivalence of quadratic extensions of global fields
On integral Witt equivalence of algebraic number fields
Automorphisms of Witt rings of global fields
We construct an uncountable set of strong automorphisms of the Witt ring of a global field.
Wild primes of a self-equivalence of a number field
Let K be a number field. Assume that the 2-rank of the ideal class group of K is equal to the 2-rank of the narrow ideal class group of K. Moreover, assume K has a unique dyadic prime and the class of is a square in the ideal class group of K. We prove that if ₁,...,ₙ are finite primes of K such that ∙ the class of is a square in the ideal class group of K for every i ∈ 1,...,n, ∙ -1 is a local square at for every nondyadic , then ₁,...,ₙ is the wild set of some self-equivalence of the field...
Kazimierz Szymiczek (1939-2015)
Wild Primes of a Higher Degree Self-Equivalence of a Number Field
Let ℓ > 2 be a prime number. Let K be a number field containing a unique ℓ-adic prime and assume that its class is an ℓth power in the class group CK. The main theorem of the paper gives a sufficient condition for a finite set of primes of K to be the wild set of some Hilbert self-equivalence of K of degree ℓ.
Page 1