Families of curves with Galois action and their \(L\)-functions

DOI10.1016/j.jnt.2015.02.015zbMath1326.11051OpenAlexW2085686852MaRDI QIDQ2343183

Cornelius Greither

Publication date: 4 May 2015

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2015.02.015

zbMATH Keywords

class groupsGalois module structureGalois coveringsFitting idealsPicard 1-motivesequivariant \(L\)-functionsmodels of relative curves

Mathematics Subject Classification ID

Geometric class field theory (11G45) Curves over finite and local fields (11G20) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Varieties over finite and local fields (11G25) (p)-adic cohomology, crystalline cohomology (14F30) Zeta and (L)-functions in characteristic (p) (11M38)

Cites Work

• Explicit points on the Legendre curve. II
• \(L\)-functions of twisted Legendre curves
• On the values of equivariant zeta functions of curves over finite fields
• Good reduction of abelian varieties
• Rational singularities, with applications to algebraic surfaces and unique factorization
• The Galois Module Structure of ℓ-adic Realizations of Picard 1-motives and Applications
• Divisor class groups of graded hypersurfaces

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