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Characterizing Serre quotients with no section functor and applications to coherent sheaves

Mohamed Barakat and Markus Lange-Hegermann,
May 2013

We prove an analogon of the the fundamental homomorphism theorem for certain classes of exact and essentially surjective functors of Abelian categories Q:A→B. It states that Q is up to equivalence the Serre quotient A→A/kerQ, even in cases when the latter does not admit a section functor. For several classes of schemes X, including projective and toric varieties, this characterization applies to the sheafification functor from a certain category A of finitely presented graded modules to the category B=CohX of coherent sheaves on X. This gives a direct proof that CohX is a Serre quotient of A.

Literature procurement: Springer
@misc{2367,
author= {Barakat, Mohamed and Lange-Hegermann, Markus},
title= {Characterizing Serre quotients with no section functor and applications to coherent sheaves},
howpublished= {},
month= {May},
year= {2013},
note= {},
}