Purity in categories of sheaves

Michael Prest, Alexander Slavik

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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; for example, we give a characterisation
of geometric pure-injectives in both the quasicoherent and non-quasicoherent
case. We also 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 eld.
Original languageEnglish
JournalMathematische Zeitschrift
Early online date30 Mar 2020
Publication statusPublished - 2020


  • scheme
  • sheaf
  • pure-extract sequence
  • Ziegler spectrum


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