Abelian Log Fundamental Group scheme

2020/12/05 by Aritra sen, sen, Aritra
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2012.02917

openalex publication_date 2020/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a connected Dedekind scheme and X be a proper smooth connected scheme over S . Let D a divisor with no multiplicity of X such that the irreducible components of D and as well their intersections are smooth over S. Now if we endow X with the log structure associated with D then the structure morphism from X to S is log-smooth. Let x: S → X be a S-point such that it doesn't intersect D. Then we prove that the maximal abelian quotient of the log Nori fundamental group scheme of X fits in to an exact sequence of the form 0 → (NS^τ_X/S,D)^\vee → (π^log_Nori(X,x))^ab → \undersetn\varprojlim Alb_X/S,D[n] → 0. Here NS^τ_X/S,D is the torsion subgroup scheme of the generalized Neron-Severi group and Alb_X/S,D is the generalized Albanese scheme associated with the divisor D.

Citations

• Logarithmic structures of Fontaine-Illusie. II

Related

• Log p-divisible groups associated with semi-abelian degeneration
• Log Fundamental Group Scheme
• On an extension of Nori and local fundamental group schemes
• Canonical Artin Stacks over Log Smooth Schemes
• Abelianization of the F-divided fundamental group scheme