Purity in categories of sheaves

2018/09/24 by Alexander Slávik, Slavik, Alexander, Mike Prest +1
Mathematics · #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1809.08981

Abstract

We consider categorical and geometric purity for sheaves of modules over a scheme satisfying some mild conditions, both for the category of all sheaves and for the category of quasicoherent sheaves. We investigate the relations between these four purities and compute a number of examples, in particular describing both the geometric and categorical Ziegler spectra for the category of quasicoherent sheaves over the projective line over a field.

Related

• Pure injective and absolutely pure sheaves
• The Pure derived category of quasi-coherent sheaves
• Classifying torsionfree classes of the category of coherent sheaves and their Serre subcategories
• The Ziegler spectrum for enriched ringoids and schemes
• Purity and 2-Calabi-Yau categories