Direct image with compact support: Difference between revisions

Revision as of 14:26, 17 April 2008

Revision as of 12:15, 19 May 2009

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==Definition==

{{Template:Images of sheaves}}

Let ''f'': ''X'' →→ ''Y'' be a [[continuous mapping]] of [[topological space]]s, and ''Sh''(–) the [[category (mathematics)|category]] of sheaves of [[abelian group]]s on a topological space. The '''direct image with compact support'''

:''f''_!: ''Sh''(''X'') → ''Sh''(''Y'')

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==Properties==

If ''f'' is proper, then ''f''_! equals ''f''_∗∗. In general, ''f''_!(''F'') is only a subsheaf of ''f''_∗∗(''F'')

==ReferenceReferences==

* {{Citation | last1=Iversen | first1=Birger | title=Cohomology of sheaves | publisher=[[Springer-Verlag]] | ___location=Berlin, New York | series=Universitext | isbn=978-3-540-16389-3 | id={{MathSciNet | id = 842190}} | year=1986}}, esp. section VII.1