Rigid cohomology and \(p\)-adic point counting

DOI10.5802/jtnb.484zbMath1087.14020OpenAlexW2318560122MaRDI QIDQ2388616

Alan G. B. Lauder

Publication date: 15 September 2005

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=JTNB_2005__17_1_169_0

zbMATH Keywords

zeta function\(p\)-adic cohomologyvarieties over finite fieldspoint counting

Mathematics Subject Classification ID

Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Varieties over finite and local fields (11G25)

Related Items (6)

A numerical approach toward the \(p\)-adic Beilinson conjecture for elliptic curves over \(\mathbb{Q}\) ⋮ Effective convergence bounds for Frobenius structures on connections ⋮ Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields ⋮ Point Counting in Families of Hyperelliptic Curves in Characteristic 2 ⋮ A Recursive Method for Computing Zeta Functions of Varieties ⋮ Frobenius action on a hypergeometric curve and an algorithm for computing values of Dwork's \(p\)-adic hypergeometric functions

Cites Work

• On exponential sums in finite fields. II
• Counting points on curves over finite fields
• Counting solutions to equations in many variables over finite fields
• Finiteness of rigid cohomology with coefficients
• On the zeta function of a hypersurface. I
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Deformation theory and the computation of zeta functions
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• On the Rationality of the Zeta Function of an Algebraic Variety
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