Tensor triangular geometry of filtered modules

Abstract

We compute the tensor triangular spectrum of perfect complexes of filtered modules over a commutative ring and deduce a classification of the thick tensor ideals. We give two proofs: one by reducing to perfect complexes of graded modules which have already been studied in the literature by Dell’Ambrogio and Stevenson (2013, 2014) and one more direct for which we develop some useful tools.