Equidistant liftings of elementary abelian Galois covers of curves
Daniele Turchetti
TL;DR
This paper investigates the conditions under which elementary abelian Galois covers of curves can be lifted equidistantly, revealing new obstructions especially for groups like Z/3Z x Z/3Z, through analysis of differential forms and ramification.
Contribution
It introduces necessary combinatorial conditions for equidistant liftings and identifies new obstructions for specific group actions in the local lifting problem.
Findings
Necessary conditions on ramification points for equidistant liftings
New obstructions to lifting actions of Z/3Z x Z/3Z
Analysis of differential forms linked to deformations
Abstract
In this paper, we discuss the local lifting problem for the action of elementary abelian groups. Studying logarithmic differential forms linked to deformations of -torsors, we show necessary conditions on the set of ramification points in order to get equidistant liftings. Such conditions of combinatoric nature lead us to show new obstructions to lifting actions of Z/3Z x Z/3Z.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Numerical Analysis Techniques · Polynomial and algebraic computation