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arXiv · 1802.00618

Separated quotients of Picard schemes

Garnet Akeyr
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Abstract

We give some necessary and sufficient conditions for the existence of N\'{e}ron models of jacobians of semistable morphisms of arbitrary relative dimension over base schemes of arbitrary dimension. To do this, we introduce a notion of alignment for semistable morphisms over any regular base scheme, and show that the jacobian of an aligned projective semistable morphism admits a separated model with the N\'{e}ron mapping property. When the Picard scheme is smooth over the base scheme along its unit section we show that the converse holds.

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Garnet Akeyr. 2018-02-02. Separated quotients of Picard schemes. https://arxiv.org/abs/1802.00618

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