Abstract:
We shall overview how the notion of modulus enables us to generalize
many aspects of motive theory. One of the earliest examples can be seen
in Laumon's generalization of the theory of Deligne 1-motives. We then
explain our construction of modulus version of the mixed Hodge structures.
As an application, we generalize Kato-Russell's construction of Albanese
varieties with modulus to 1-motives. This is joint work with Ivorra.