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Picard schemes of acyclic schemes

2017/06/28 by Jason Starr, Jason Michael Starr, Starr, Jason Michael
Mathematics · #14C22 #14M10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #math.AG #msc:14C22 #msc:14M10

paper · pdf · doi:10.48550/arxiv.1706.09327

10 pp

arxiv created 2017/06/28 · openalex publication_date 2017/06/28 · arxiv updated 2017/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In his work extending rational simple connectedness to schemes with higher Picard rank, Yi Zhu introduced hypotheses for schemes insuring that the relative Picard functor is representable and is étale locally constant with finite free stalks. We give examples showing that one cannot eliminate any of the hypotheses and still have a representable Picard functor that is locally constant with finite free stalks. We also prove that the hypotheses are compatible with composition and with hyperplane sections.

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