author:
======= 
Shigeo Koshitani 
Jürgen Müller

title:
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The projective cover of the trivial representation
for a finite group of Lie type in defining characteristic

abstract:
========= 
We give a lower bound of the Loewy length of the projective cover of
the trivial module for the group algebras kG of a finite group G of Lie 
type defined over a finite field of odd characteristic p, where k is an 
arbitrary field of characteristic p; the proof uses Auslander-Reiten theory.
We point out that in one of the main results of a recent paper by
Lübeck-Malle [2016] there is a gap, implying that contrary to the claim made 
there a question asked in Koshitani-Külshammer-Sambale [2014] is still open.

status: 
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submitted