Improvements to the deformation method for counting points on smooth projective hypersurfaces

DOI10.1007/s10208-014-9242-8zbMath1400.11128arXiv1307.1250OpenAlexW2023046297MaRDI QIDQ895704

Jan Tuitman, Sebastian Pancratz

Publication date: 4 December 2015

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.1250

zbMATH Keywords

finite fieldscomputing zeta functionsdeformation method

Mathematics Subject Classification ID

Computational aspects of algebraic surfaces (14Q10) Number-theoretic algorithms; complexity (11Y16) Zeta and (L)-functions in characteristic (p) (11M38)

Related Items (9)

Counting points with Berglund–Hübsch–Krawitz mirror symmetry ⋮ Computing zeta functions of arithmetic schemes ⋮ Zeta functions of monomial deformations of Delsarte hypersurfaces ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Point counting on K3 surfaces and an application concerning real and complex multiplication ⋮ Computing zeta functions of generic projective hypersurfaces in larger characteristic ⋮ Counting points on curves using a map to $\mathbf {P}^1$ ⋮ A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants ⋮ Computing periods of hypersurfaces

Uses Software

• FLINT

Cites Work

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