Bloch's formula for 0-cycles with modulus and higher dimensional Class Field Theory

2020/02/05 by Federico Binda, Binda, Federico, Amalendu Krishna +3 · 1 citation
Mathematics · #14C25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 19E15 #Secondary 14F42

paper · pdf · doi:10.48550/arxiv.2002.01856

openalex publication_date 2020/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Bloch's formula for the Chow group of 0-cycles with modulus on a smooth quasi-projective surface over a field. We use this formula to give a simple proof of the rank one case of a conjecture of Deligne and Drinfeld on lisse ℚ_ℓ-sheaves. This was originally solved by Kerz and Saito in characteristic ≠ 2.

Cited by

• The Pythagoras number of fields of transcendence degree 1 over ℚ

Related

• Idele class groups with modulus
• On 0-cycles with modulus
• K-theory and 0-cycles on schemes
• 0-cycles on singular schemes and class field theory
• Bloch's conjecture on surfaces of general type with p_g=q=0, K²=3 and with an involution