On a theorem of M. Deuring and I. R. Šafarevič

DOI10.1007/BF01168587zbMath0369.12011OpenAlexW2001476362MaRDI QIDQ1243761

Manohar L. Madan

Publication date: 1977

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/154509

zbMATH Keywords

Galois cohomology\(\ell\)-ranks of the null class groupsfield of algebraic functions of one variablemodified Deuring's method of proof

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Galois cohomology (12G05) Class numbers, class groups, discriminants (11R29) Galois cohomology (11R34)

Related Items (14)

Structure of semisimple differentials and p-class groups in \({\mathbb{Z}}_ p\)-extensions ⋮ On geometric \({\mathbb{Z}}_ p\)-extensions of function fields ⋮ Hyperelliptic curves over 𝔽₂ of every 2-rank without extra automorphisms ⋮ A new family of maximal curves over a finite field ⋮ Galois module structure of Jacobians in unramified extensions ⋮ Integral representations of p-class groups in \({\mathbb{Z}}_ p\)-extensions, semisimple differentials and Jacobians ⋮ Some remarks on the p-rank of an algebraic curve ⋮ On the Deuring-Shafarevich formula ⋮ Über einen Satz von Deuring-Safarevic-Madan ⋮ Class group rank relations in \(Z_p\)-extensions ⋮ Hasse-Witt-invariants and dihedral extensions ⋮ An application of a theorem of Deuring and Šafarevič ⋮ Some \(p\)-adic Galois representations for curves in characteristic \(p\) ⋮ Equivariant form of the Deuring-Šafarevič formula for Hasse-Witt invariants

Cites Work

• Unnamed Item
• The p-rank of Artin-Schreier curves
• \(p\)-torsion in the class group of curves with too many automorphisms
• Ambiguous divisor classes in function fields
• Class number and ramification in fields of algebraic functions

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