A user's guide to the local arithmetic of hyperelliptic curves

DOI10.1112/blms.12604arXiv2007.01749OpenAlexW3039850483MaRDI QIDQ6133372

Matthew Bisatt, Vladimir Dokchitser, Céline Maistret, Raymond Van Bommel, Sarah Nowell, Omri Faraggi, Adam Morgan, Unnamed Author, Unnamed Author, Unnamed Author, Sabrina Kunzweiler

Publication date: 18 August 2023

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.01749

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Special algebraic curves and curves of low genus (14H45) Curves over finite and local fields (11G20) Arithmetic ground fields (finite, local, global) and families or fibrations (14D10) Local ground fields in algebraic geometry (14G20) Computational aspects of algebraic curves (14Q05)

Related Items (6)

Galois representations of superelliptic curves ⋮ 2‐Selmer parity for hyperelliptic curves in quadratic extensions ⋮ Arithmetic of hyperelliptic curves over local fields ⋮ Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction ⋮ Root number of the Jacobian of \(y^2 = x^p+a\) ⋮ A note on hyperelliptic curves with ordinary reduction over 2-adic fields

Cites Work

• Unnamed Item
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• Clusters, inertia, and root numbers
• Variation of Tamagawa numbers of Jacobians of hyperelliptic curves with semistable reduction
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• Arithmetic of hyperelliptic curves over local fields
• COMPUTINGL-FUNCTIONS AND SEMISTABLE REDUCTION OF SUPERELLIPTIC CURVES
• Modèles entiers des courbes hyperelliptiques sur un corps de valuation discrète
• 3-torsion and conductor of genus 2 curves
• Wild Galois representations: a family of hyperelliptic curves with large inertia image
• Models of hyperelliptic curves with tame potentially semistable reduction
• Explicit resolution of weak wild quotient singularities on arithmetic surfaces
• Constructing hyperelliptic curves with surjective Galois representations
• Semistable types of hyperelliptic curves
• Explicit root numbers of abelian varieties
• Tate module and bad reduction

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