Constructible -Motives and Exactness of Realisation Functors
Simon Pepin LehalleurFreie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany
The triangulated category of cohomological -motives with rational coefficients over a base scheme admits a motivic t-structure. We prove that this t-structure restricts to the subcategory of compact objects, and that pullbacks along arbitrary morphisms, as well as Betti and étale realisation functors, are t-exact relative to this t-structure. These exactness properties follow from a structural result: compact objects in the heart behave like a constructible sheaf of Deligne -motives.
Cite this article
Simon Pepin Lehalleur, Constructible -Motives and Exactness of Realisation Functors. Doc. Math. 24 (2019), pp. 1721–1737DOI 10.4171/DM/713