\(S\)-units and \(S\)-class group in algebraic function fields

DOI10.1016/0021-8693(73)90036-7zbMath0265.12003OpenAlexW2034877958MaRDI QIDQ2562213

Michael I. Rosen

Publication date: 1973

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(73)90036-7

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Units and factorization (11R27) Class numbers, class groups, discriminants (11R29) Global ground fields in algebraic geometry (14G25) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (29)

Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields ⋮ Homology of \(\operatorname{SL}_2\) over function fields. I: Parabolic subcomplexes ⋮ On an analogue of a conjecture of Gross ⋮ On the class groups of pure function fields ⋮ Every abelian group is the class group of a simple Dedekind domain ⋮ Idéaux ambiges dans les corps de fonctions. (Ambiguous ideals in function fields) ⋮ The class number of cyclotomic function fields ⋮ Units and class groups in cyclotomic function fields ⋮ Cohen-Lenstra heuristics and the Spiegelungssatz: function fields ⋮ The genus field of an algebraic function field ⋮ Toric varieties from cyclic matrix semigroups ⋮ Reflection theorem for divisor class groups of relative quadratic function fields ⋮ Gauss problem for function fields ⋮ Cyclotomic function fields with ideal class number one ⋮ Rabinowitsch times six ⋮ A note on ray class fields of global fields ⋮ Witt rings of Hasse domains of global fields ⋮ The rank of abelian varieties over infinite Galois extensions ⋮ The Scholz theorem in function fields ⋮ Unimodular quadratic forms over global function fields ⋮ Class numbers of real quadratic function fields of genus one ⋮ On the class numbers of the maximal real subfields of cyclotomic function fields ⋮ The asymptotic behavior of automorphism groups of function fields over finite fields ⋮ On the class numbers of the maximal real subfields of cyclotomic function fields. II ⋮ Elliptic Curves and Dedekind Domains ⋮ Class number one problem for imaginary function fields: the cyclic prime power case ⋮ Affine curves on which every point is a set-theoretic complete intersection ⋮ The distribution of class groups of function fields ⋮ Hypersurfaces in projective schemes and a moving lemma

Cites Work

• Analytische Zahlentheorie in Körpern der Charakteristik \(p\)
• Every Abelian group is a class group
• Principal Homogeneous Spaces Over Abelian Varieties
• Diophantine Equations with Special Reference To Elliptic Curves
• Axiomatic characterization of fields by the product formula for valuations
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