Abstract
The goal of this paper is to extend the work of Voevodsky and Morel on the homotopy t-structure on the category of motivic complexes to the context of motives for logarithmic schemes. To do so, we prove an analogue of Morel's connectivity theorem and show a purity statement for (P$^{1}$,∞)-local complexes of sheaves with log transfers.
The homotopy t-structure on logDM$^{eff}$(k) is proved to be compatible with Voevodsky's t-structure i.e. we show that the comparison functor R$^{□}$ω$^{∗}$:DM$^{eff}$(k)→logDM$^{eff}$(k) is t-exact.
The heart of the homotopy t-structure on logDM$^{eff}$(k) is the Grothendieck abelian category of strictly cube-invariant sheaves with log transfers: we use it to build a new version of the category of reciprocity sheaves in the style of Kahn--Saito--Yamazaki and Rülling.
Binda, Federico