On geometric \({\mathbb{Z}}_ p\)-extensions of function fields

DOI10.1007/BF01278975zbMath0662.12016OpenAlexW2044744102MaRDI QIDQ1113949

S. H. Smith

Publication date: 1988

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

Full work available at URL: https://eudml.org/doc/155337

zbMATH Keywords

Iwasawa theoryextensions of function fieldsgrowth of the class number

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Cyclotomic extensions (11R18)

Related Items (11)

Class number growth of a family of \(\mathbb{Z}_p\)-extensions over global function fields ⋮ IWASAWA THEORY FORp-TORSION CLASS GROUP SCHEMES IN CHARACTERISTICp ⋮ On \(\mathbb{Z}_{\ell}^d\)-towers of graphs ⋮ Aspects of Iwasawa theory over function fields ⋮ On Geometric Iwasawa Theory and Special Values of Zeta Functions ⋮ \(p\)-adic Wan-Riemann hypothesis for \(\mathbb{Z}_p\)-towers of curves ⋮ On the \(\mu\)-invariants of abelian varieties over function fields of positive characteristic ⋮ Gauss sums for function fields ⋮ Class numbers and \(p\)-ranks in $\mathbb{Z}_p^d$-towers ⋮ Class numbers of cyclotomic function fields ⋮ Genus growth in $\mathbb {Z}_p$-towers of function fields

Cites Work

• Some remarks on the p-rank of an algebraic curve
• Class group rank relations in \(Z_p\)-extensions
• Ambiguous divisor classes in function fields
• On a theorem of M. Deuring and I. R. Šafarevič
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• On the theory of congruence function fields
• Zur Geschlechtertheorie in abelschen Zahlkörpern
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