Some Further Remarks on the Local Fundamental Group Scheme

TL;DR

This paper demonstrates that the Local Fundamental Group Scheme adheres to Lefschetz-Bott theorems in characteristic p, utilizing classical vanishing theorems and properties of p-curvature.

Contribution

It establishes the Lefschetz-Bott theorems for the Local Fundamental Group Scheme in characteristic p, extending classical results to this setting.

Findings

Lefschetz-Bott theorems hold for the Local Fundamental Group Scheme in characteristic p

Standard vanishing theorems are applicable in this context

Known properties of p-curvature are used in the proofs

Abstract

We prove that the Local Fundamental Group Scheme satisfies the Lefschetz - Bott theorems in characteristic p. The proofs are standard applications of the Enriques-Severi -Zariski-Serre vanishing theorems and known facts about the p-curvature