Function field genus theory for non-Kummer extensions
Copyright policy )Function field genus theory for non-Kummer extensions
In this paper we first obtain the genus field of a finite abelian non-Kummer $l$--extension of a global rational function field. Then, using that the genus field of a composite of two abelian extensions of a global rational function field with relatively prime degrees is equal to the composite of their respective genus fields and our previous results, we deduce the general expression of the genus field of a finite abelian extension of a global rational function field.
11 pages
Arithmetic theory of algebraic function fields, Mathematics - Number Theory, Cyclotomic function fields (class groups, Bernoulli objects, etc.), global fields, Primary 11R58, Secondary 11R29, 11R60, Class numbers, class groups, discriminants, non-Kummer extensions, FOS: Mathematics, cyclic extensions, Number Theory (math.NT), genus fields, abelian extensions
Arithmetic theory of algebraic function fields, Mathematics - Number Theory, Cyclotomic function fields (class groups, Bernoulli objects, etc.), global fields, Primary 11R58, Secondary 11R29, 11R60, Class numbers, class groups, discriminants, non-Kummer extensions, FOS: Mathematics, cyclic extensions, Number Theory (math.NT), genus fields, abelian extensions
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!