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Deligne cohomology : ウィキペディア英語版
Deligne cohomology
In mathematics, Deligne cohomology is the hypercohomology of the Deligne complex of a complex manifold. It was introduced by Pierre Deligne in unpublished work in about 1972 as a cohomology theory for algebraic varieties that includes both ordinary cohomology and intermediate Jacobians.
For introductory accounts of Deligne cohomology see , , and .
==Definition==

The analytic Deligne complex Z(''p'')D, an on a complex analytic manifold ''X'' is
:0\rightarrow \mathbf Z(p)\rightarrow \Omega^0_X\rightarrow \Omega^1_X\rightarrow\cdots\rightarrow \Omega_X^ \rightarrow 0 \rightarrow \dots
where Z(''p'') = (2π i)''p''Z. Depending on the context, \Omega^
*_X is either the complex of smooth (i.e., ''C'') differential forms or of holomorphic forms, respectively.
The Deligne cohomology is the ''q''-th hypercohomology of the Deligne complex.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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