University of Chicago
Department of Mathematics

Slope filtrations occur in algebraic and analytic geometry (coherent sheaves, motives...), in asymptotic analysis, in ramification theory, in geometry of numbers, in several p-adic theories... These functorial filtratio ns, which are indexed by rational (or sometimes real) numbers, have a lot of com mon properties. We shall outline a unified treatment of slope filtrations, with the aim of fre eing the ``yoga of stability" from any ad hoc property of the underlying categor y. We shall describe a number of examples and survey how new ties between diffe rent domains have been woven by dint of deep correspondences between different c oncrete slope filtrations