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 Alblog(X) that extends Serre's semi-abelian Albanese variety of X_−|∂X|. This generalizes the higher Albanese sheaves of Ayoub, Barbieri-Viale and Kahn and is related to an old question of Grothendieck.
Derived log Albanese sheaves / F. Binda, A. Merici, S. Saito. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 417:(2023 Mar 15), pp. 108936.1-108936.85. [10.1016/j.aim.2023.108936]
Derived log Albanese sheaves
F. Binda
Primo
;
2023
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 Alblog(X) that extends Serre's semi-abelian Albanese variety of X_−|∂X|. This generalizes the higher Albanese sheaves of Ayoub, Barbieri-Viale and Kahn and is related to an old question of Grothendieck.
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