Semi-continuity for total dimension divisors of \'etale sheaves
Haoyu Hu, Enlin Yang
TL;DR
This paper extends semi-continuity properties of total dimension divisors of étale sheaves from curves to higher dimensions, providing a generalized inequality and broadening the understanding of Swan conductors in algebraic geometry.
Contribution
It introduces a new pull-back inequality for total dimension divisors and generalizes semi-continuity results to higher-dimensional relative schemes.
Findings
Extended semi-continuity of Swan conductors to higher dimensions
Established a pull-back inequality for total dimension divisors
Generalized results previously known for curves
Abstract
In this article, we extend a pull-back inequality for total dimension divisors of \'etale sheavs due to Saito. Using this formula, we generalize Deligne and Laumon's lower semi-continuous property for Swan conductors of \'etale sheaves on relative curves to higher relative dimensions in a geometric situation.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology