Counting solutions to equations in many variables over finite fields

DOI10.1007/s10208-003-0093-yzbMath1076.11040OpenAlexW2000578879MaRDI QIDQ1767486

Alan G. B. Lauder

Publication date: 11 March 2005

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

Full work available at URL: https://doi.org/10.1007/s10208-003-0093-y

zbMATH Keywords

algorithmfinite fielddeformation theoryzeta functionhomogeneous polynomialprojective hypersurfaceDwork cohomology

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Counting solutions of Diophantine equations (11D45) Finite ground fields in algebraic geometry (14G15) Varieties over finite and local fields (11G25) (p)-adic cohomology, crystalline cohomology (14F30) Zeta and (L)-functions in characteristic (p) (11M38)

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Rigid cohomology and \(p\)-adic point counting ⋮ Computing zeta functions of arithmetic schemes ⋮ Improvements to the deformation method for counting points on smooth projective hypersurfaces ⋮ Faster \(p\)-adic feasibility for certain multivariate sparse polynomials ⋮ Counting roots for polynomials modulo prime powers ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Point Counting on Singular Hypersurfaces ⋮ Nonstandard rank-one nonincreasing maps on symmetric matrices ⋮ Fast arithmetic in unramified \(p\)-adic fields ⋮ Computing zeta functions of generic projective hypersurfaces in larger characteristic ⋮ Unnamed Item ⋮ A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants ⋮ Randomized polynomial-time root counting in prime power rings ⋮ A Recursive Method for Computing Zeta Functions of Varieties

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