Abelian Log Fundamental Group scheme
Aritra sen

TL;DR
This paper studies the abelianized log Nori fundamental group scheme of a smooth proper scheme over a Dedekind scheme with a divisor, establishing an exact sequence involving Neron-Severi and Albanese schemes.
Contribution
It provides a new exact sequence describing the maximal abelian quotient of the log Nori fundamental group scheme in terms of generalized Neron-Severi and Albanese schemes.
Findings
Established an exact sequence for the abelianized log Nori fundamental group scheme.
Connected the fundamental group scheme with Neron-Severi and Albanese schemes.
Extended classical fundamental group concepts to the logarithmic setting.
Abstract
Let be a connected Dedekind scheme and be a proper smooth connected scheme over . Let a divisor with no multiplicity of such that the irreducible components of and as well their intersections are smooth over . Now if we endow with the log structure associated with then the structure morphism from to is log-smooth. Let be a -point such that it doesn't intersect . Then we prove that the maximal abelian quotient of the log Nori fundamental group scheme of fits in to an exact sequence of the form . Here is the torsion subgroup scheme of the generalized Neron-Severi group and is the…
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
