Lines on Cubic Hypersurfaces Over Finite Fields

DOI10.1007/978-3-319-49763-1_2zbMath1448.14022arXiv1510.05803OpenAlexW1766764775MaRDI QIDQ4645315

Olivier Debarre, Xavier Roulleau, Antonio Laface

Publication date: 10 January 2019

Published in: Geometry Over Nonclosed Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.05803

zbMATH Keywords

finite fieldsFano varietyzeta functionscubic hypersurfacesTate conjecturelines in hypersurfaces

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Hypersurfaces and algebraic geometry (14J70)

Related Items (4)

Irrationality of generic cubic threefold via Weil's conjectures ⋮ Rational lines on cubic hypersurfaces ⋮ A probabilistic approach to systems of parameters and Noether normalization ⋮ Binary curves of small fixed genus and gonality with many rational points

Uses Software

• Magma
• GitHub

Cites Work

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• The moduli space of cubic threefolds via degenerations of the intermediate Jacobian
• Variétés de Prym et jacobiennes intermédiaires
• La conjecture de Tate entière pour les cubiques de dimension quatre
• Effective 𝑝-adic cohomology for cyclic cubic threefolds
• Numbers of solutions of equations in finite fields
• On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field
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