  We explain how some results of M. Nori (on motives) and F. Ivorra (on
perverse motives) can be used to define "motivic" versions of Lyubeznik
numbers, a set of numerical invariants for local rings. We also discuss on
additional structures that might be put on some local cohomology modules
(besides those of D- or F-module). This note is mainly expository, it is an
expanded version of my talk at the FACARD workshop in Barcelona, on January
2019.
