Definition of torsion sheaf on reducible spaces - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T01:24:55Z http://mathoverflow.net/feeds/question/108032 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/108032/definition-of-torsion-sheaf-on-reducible-spaces Definition of torsion sheaf on reducible spaces Stefan Kebekus 2012-09-25T09:23:58Z 2012-09-25T09:44:17Z <p>I need to discuss torsion-free sheaves on reduced, but possibly reducible spaces. Here "torsion" means "element is annihilated by a non-zero-divisor". The standard references (EGA, Hartshorne, ...) restrict themselves to normal varieties or irreducible spaces and do not seem to cover the definition in this level of generality. </p> <p>I saw some papers and survey articles that use torsion-free sheaves on reducibly spaces, but mostly without any discussion of the definition. Some papers even seem to give the "wrong" definition where "torsion" = "annihilated arbitrary non-zero element", which is probably not what the authors had in mind.</p> <p>Is anyone aware of a reliable reference for the definition and for basic properties of torsion-free sheaves that I could possibly use?</p> <p>Thank you in advance!</p> http://mathoverflow.net/questions/108032/definition-of-torsion-sheaf-on-reducible-spaces/108036#108036 Answer by Angelo for Definition of torsion sheaf on reducible spaces Angelo 2012-09-25T09:44:17Z 2012-09-25T09:44:17Z <p>Hi Stefan! Torsion-free (coherent) sheaves are pure sheaves of codimension 0; I suggest that you try "The Geometry of Moduli Spaces of Sheaves", by Daniel Huybrechts and Manfred Lehn, where pure sheaves are discussed in detail.</p>