- In
homological algebra, the
hyperhomology or
hypercohomology ( H ∗ ( − ) , H ∗ ( − ) {\displaystyle \mathbb {H} _{*}(-),\mathbb {H} ^{*}(-)} ) is a generalization...
-
Deligne cohomology sometimes called Deligne-Beilinson
cohomology is the
hypercohomology of the
Deligne complex of a
complex manifold. It was
introduced by...
-
functors can then be
defined for
chain complexes,
refining the
concept of
hypercohomology. The
definitions lead to a
significant simplification of
formulas otherwise...
-
second pages of the
hypercohomology spectral sequences for both of them only have one
nonzero column each, thus the
hypercohomologies of the two complexes...
-
space X with
coefficients in any
complex of sheaves,
earlier called hypercohomology (but
usually now just "cohomology"). From that
point of view, sheaf...
- of the
derived category, so the
cohomology on the
right means the
hypercohomology of the complex). The
complex I C p ( X ) {\displaystyle IC_{p}(X)}...
-
coalgebra structure inherited from the one on the
exterior algebra. The
hypercohomology of the de Rham
complex of
sheaves is
called the
algebraic de Rham cohomology...
-
cohomology of Z over the
formal scheme of W (an
inverse limit of the
hypercohomology of the
complexes of
differential forms).
Conversely the de Rham cohomology...
- the
existence of
motivic cohomology groups for schemes,
provided as
hypercohomology groups of a
complex of
abelian groups and
related to
algebraic K-theory...
- {\text{Sh}}_{\underline {A}}(X)} . Then, one
replaces sheaf cohomology with
sheaf hypercohomology. The
existence of the
Leray spectral sequence is a
direct application...
