Resumen de Brauer-friendly modules and slash functors

Erwan Biland

• This paper introduces the notion of Brauer-friendly modules , a generalisation of endo-p -permutation modules. A module over a block algebra OGeOGe is said to be Brauer-friendly if it is a direct sum of indecomposable modules with compatible fusion-stable endopermutation sources. We obtain, for these modules, a functorial version of Dade's slash construction, also known as deflation�restriction. We prove that our slash functors , defined over Brauer-friendly categories , share most of the very useful properties that are satisfied by the Brauer functor over the category of p -permutation OGe-modulesOGe-modules. In particular, we give a parametrisation of indecomposable Brauer-friendly modules, which opens the way to a complete classification whenever the fusion-stable sources are classified. Those tools have been used by the author in [4] to prove the existence of a stable equivalence between non-principal blocks in the context of a minimal counterexample to the odd Zp?-theorem.