Finite generation of lifted p-adic homology with compact supports. Generalization of the Weil conjectures to singular, non-complete algebraic varieties

DOI10.1016/0022-314X(79)90010-6zbMath0445.14011OpenAlexW2147614094WikidataQ123224936 ScholiaQ123224936MaRDI QIDQ1145184

Saul Lubkin

Publication date: 1979

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-314x(79)90010-6

zbMATH Keywords

Riemann hypothesisWeil conjectureq-adic homology with compact supportssingular varieties over finite fieldsWeil Lefschetz theorem conjecturezeta matrices

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) (p)-adic cohomology, crystalline cohomology (14F30) Arithmetic problems in algebraic geometry; Diophantine geometry (14G99)

Related Items

Géométrie rigide et cohomologie des variétés algébriques de caractéristique $p$ ⋮ Zeta matrices of elliptic curves ⋮ On the Generators of the First Homology with Compact Supports of the Weierstrass Family in Characteristic Zero ⋮ Schrödinger's cat ⋮ Lifted p-adic homology with compact supports of the Weierstrass family and its zeta endomorphism

Cites Work

• La conjecture de Weil. I
• A \(p\)-adic proof of Weil's conjectures
• A generalization of the imbedding problem of an abstract variety in a complete variety
• Second Leray spectral sequence of relative hypercohomology
• On the Rationality of the Zeta Function of an Algebraic Variety
• On a Conjecture of Andre Weil
• Numbers of solutions of equations in finite fields
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