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 $X=(\underline{X},\partial X)$. The result involves an inverse system of the coherent cohomology of the underlying scheme as well as a pro-group scheme ${\mathrm{Alb}}^{\log }(X)$ that extends Serre's semi-abelian Albanese variety of $\underline{X}-|\partial X|$. This generalizes the higher Albanese sheaves of Ayoub, Barbieri-Viale and Kahn.

61 pages: final version. To appear in Advances in Mathematics

References in corpus (6)

• Zero cycles with modulus and zero cycles on singular varieties
• 1-motivic sheaves and the Albanese functor
• Birational motives, II: Triangulated birational motives
• Reciprocity sheaves and logarithmic motives
• Integral morphisms and log blow-ups
• Motivic interpretation of Albanese varieties of smooth varieties