Realizing Artin-Schreier covers with minimal \(a\)-numbers in positive characteristic

DOI10.2140/involve.2022.15.559OpenAlexW4320016706MaRDI QIDQ2681306

Miroslav Marinov, Paweł Narkiewicz, Hugo Berg, Viktor Fukala, Nancy Xu, Fiona Abney-McPeek, Theo Müller, Rachel J. Pries, Jeremy Booher, Sun Mee Choi, Andrew Yuan

Publication date: 8 February 2023

Published in: Involve (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.09028

zbMATH Keywords

Jacobianfinite fieldcurveCartier operator\(p\)-rank\(p\)-torsionarithmetic geometrywild ramificationArtin-Schreier cover\(a\)-numberformal patchingcharacteristic-\(p\)

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Polynomials in number theory (11C08) Jacobians, Prym varieties (14H40) Curves over finite and local fields (11G20) Polynomials over finite fields (11T06) Coverings of curves, fundamental group (14H30) Linear transformations, semilinear transformations (15A04) Formal methods and deformations in algebraic geometry (14D15) Positive characteristic ground fields in algebraic geometry (14G17)

Related Items (2)

IWASAWA THEORY FORp-TORSION CLASS GROUP SCHEMES IN CHARACTERISTICp ⋮ Realizing Artin-Schreier covers of curves with minimal Newton polygons in positive characteristic

Cites Work

• Ekedahl-Oort strata of hyperelliptic curves in characteristic 2
• The \(p\)-rank stratification of Artin-Schreier curves
• The p-rank of Artin-Schreier curves
• Patching and thickening problems
• The Magma algebra system. I: The user language
• Realizing Artin-Schreier covers of curves with minimal Newton polygons in positive characteristic
• Families of Artin-Schreier curves with Cartier-Manin matrix of constant rank
• Algebraic Function Fields and Codes
• A note on algebraic curves in characteristic 2
• Néron Models
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