Nonstandard Point Counting for Algebraic Varieties

DOI10.1080/00927872.2012.737074zbMath1273.14011OpenAlexW2032100053MaRDI QIDQ2839088

Nobuyoshi Takahashi

Publication date: 4 July 2013

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927872.2012.737074

zbMATH Keywords

motivic zeta functionmotivic measurealgebraic dynamical system

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Foundations of algebraic geometry (14A99)

Cites Work

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• Chow groups are finite dimensional, in some sense
• Positive motivic measures are counting measures
• Non-standard tight closure for affine \(\mathbb C\)-algebras
• Stringy zeta functions for \(\mathbb Q\)-Gorenstein varieties
• La conjecture de Weil. I
• Über die Dichte der Primzahlen \(p\), für die eine vorgegebene ganzrationale Zahl \(a\neq 0\) von durch eine vorgegebene Primzahl \(l\neq 2\) teilbarer bzw. unteilbarer Ordnung \(\mod p\) ist
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Torification and factorization of birational maps
• Number of Points of Varieties in Finite Fields

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