On centrally generically tame algebras over perfect fields

Abstract

We show that the central generic tameness of a finite-dimensional algebra Λover a (possibly finite) perfect field, is equivalent to its non-almost sharp wildness. In this case: we give, for each natural number d, parametrizations of the indecomposable Λ-modules with central endolength d, modulo finite scalar extensions, over rational algebras. Moreover, we show that the central generic tameness of Λis equivalent to its semigeneric tameness, and that in this case, algebraic boundedness coincides with central finiteness for generic Λ-modules.