On the Log-Picard functor for aligned degenerations of curves

Abstract

We show that a particular subfunctor of the relative logarithmic Picard functor for families of aligned, log semistable curves over a regular base scheme and smooth over an open dense subscheme of the base is representable by a smooth algebraic space which is slightly more separated than the classical relative Picard functor. We show the existence of its maximal separated quotient and give a new functorial interpretation in terms of logarithmic geometry for the N\'eron model of the relative Picard functor of the smooth locus when we restrict to transversal pull backs from spectra of discrete valuation rings. We also show that aligned degenerations are log cohomologically flat.