Genus fields of congruence function fields
Copyright policy )Genus fields of congruence function fields
Let $k$ be a rational congruence function field and consider an arbitrary finite separable extension $K/k$. If for each prime in $k$ ramified in $K$ we have that at least one ramification index is not divided by the characteristic of $K$, we find the genus field $\g K$, except for constants, of the extension $K/k$. In general, we describe the genus field of a global function field.
16 pages
Arithmetic theory of algebraic function fields, Mathematics - Number Theory, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Class numbers, class groups, discriminants, global function fields, cyclotomic function fields, FOS: Mathematics, Number Theory (math.NT), genus fields, Primary 11R60, Secondary 11R58, 11R29
Arithmetic theory of algebraic function fields, Mathematics - Number Theory, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Class numbers, class groups, discriminants, global function fields, cyclotomic function fields, FOS: Mathematics, Number Theory (math.NT), genus fields, Primary 11R60, Secondary 11R58, 11R29
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