The Homotopy Sequence of Nori's Fundamental Group
Lei Zhang

TL;DR
This paper studies the conditions for the exactness of Nori's fundamental group sequence, applying them to classical theorems and providing counterexamples to illustrate when conditions fail.
Contribution
It establishes necessary and sufficient conditions for the exactness of Nori's fundamental group sequence and explores their implications in various contexts.
Findings
Identified conditions under which the homotopy sequence is exact
Reproved classical theorems using these conditions
Provided a counterexample where conditions are not met
Abstract
In this paper, we investigate the necessary sufficient conditions for the exactness of the homotopy sequence of Nori's fundamental group and apply these to various special situations to regain some classical theorems and give a counter example to show the conditions are not always satisfied. This work partially bases on the earlier work of H.Esnault, P.H.Hai, E.Viehweg.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
