Derived Log Albanese Sheaves

Abstract

We define higher pro-Albanese functors for every effective log motive over a field k of characteristic zero, and we compute them for every smooth log smooth scheme X = (X, ∂X). The result involves an inverse system of the coherent cohomology of the underlying scheme as well as a pro-group scheme Alb log (X) that extends Serre's semiabelian Albanese variety of X − |∂X|. This generalizes the higher Albanese sheaves of Ayoub, Barbieri-Viale and Kahn.