Local-global principles for the existence of Levi factors
David Harbater, Julia Hartmann, and George McNinch
TL;DR
This paper investigates local-global principles for Levi factors in linear algebraic groups over function fields, providing examples of failures and conditions for success.
Contribution
It introduces new examples of disconnected groups failing the local-global principle and establishes a strong principle under Levi descent conditions.
Findings
Disconnected groups can fail the local-global principle
A strong local-global principle holds with Levi descent
Examples illustrate the limits of existing principles
Abstract
We discuss local-global principles for the existence of Levi factors (i.e., complements to the unipotent radical) for linear algebraic groups over one-variable function fields. We give examples of disconnected groups that fail the local-global principle, and prove a strong local-global principle in the presence of Levi descent.
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