TL;DR
This paper establishes foundational structural results for spherical varieties across different characteristics, focusing on Luna's localization, spherical roots, colors, and introducing a preliminary p-spherical system.
Contribution
It provides new insights into the structure of spherical varieties and proposes a preliminary definition of p-spherical systems, expanding the theoretical framework.
Findings
Analysis of Luna's localization in arbitrary characteristic
Characterization of spherical roots and colors
Proposal of a preliminary p-spherical system
Abstract
We prove some fundamental structural results for spherical varieties in arbitrary characteristic. In particular, we study Luna's two types of localization and use it to analyze spherical roots, colors and their interrelation. At the end, we propose a preliminary definition of a p-spherical system.
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