Which algebraic groups are Picard varieties?

2013/10/01 by Michel Brion, Brion, Michel · 2 citations
Computer Science · Mathematics · #14C22 #14L10 #14L15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.1310.0186

openalex publication_date 2013/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that every connected commutative algebraic group over an algebraically closed field of characteristic 0 is the Picard variety of some projective variety, obtained by pinching a smooth variety along a finite subscheme. In contrast, no Witt group of dimension at least 3 over a perfect field of prime characteristic is isogenous to the Picard variety obtained by this construction.

Cited by

• Lichtenbaum-van Hamel duality for singular varieties over p-adic fields
• Singular varieties and infinitesimal non-commutative Witt vectors

Related

• The Picard Group of Simply Connected Regular Varieties and Stratified Line Bundles
• Picard groups for line bundles with connection
• Picard Groups of Some Quot Schemes
• Projective homogeneous varieties of Picard rank one in small characteristic
• Picard Groups Of Algebraic Groups And An Affineness Criterion