Infinitesimal part of Weak Lefschetz using Milnor K- theory

2018/01/25 by Jagannathan Arjun Sathyamoorthy, Sathyamoorthy, Jagannathan Arjun
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1801.08610

openalex publication_date 2018/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective variety over a field of characteristic 0 and L an ample divisor. In this paper we study the Weak Lefschetz conjecture for Chow groups using the technique employed by Grothendieck in his study of the problem for Picard groups, and using Bloch's formula to interpret Chow groups in terms of Milnor K- theory we prove the infinitesimal part of the conjecture.

Related

• Grothendieck's standard conjecture of Lefschetz type over finite fields
• Push-forwards of Chow groups of smooth ample divisors
• Lefschetz for local Picard groups
• Motivic Lefschetz theorem for twisted Milnor hypersurfaces
• Remarks on Milnor K-theory and Tate's conjecture for divisors