- In mathematics, and in
particular homotopy theory, a
hypercovering (or hypercover) is a
simplicial object that
generalises the Čech
nerve of a cover....
- k + 1 ( X ) ≇ 0 {\displaystyle {\tilde {H}}_{k+1}(X)\not \cong 0} .
Hypercovering Aleksandroff, P. S. (1928). "Über den
allgemeinen Dimensionsbegriff...
-
French Alma mater
University of
Paris Known for
Verdier duality Verdier hypercovering theorem Artin–Verdier
duality Serre–Grothendieck–Verdier
duality Derived...
-
cohomology groups. To get
around this, Jean-Louis
Verdier developed hypercoverings.
Hypercoverings not only give the
correct higher cohomology groups but also...
- has
fiber products. The
coskeleton is
needed to
define the
concept of
hypercovering in
homotopical algebra and
algebraic geometry.
Peter McMullen, Egon...
- {U}}\to {\mathcal {U}}\times _{X}{\mathcal {U}}\to {\mathcal {U}}.} A
hypercovering K∗ of X is a
certain simplicial object in C, i.e., a
collection of objects...
-
topos theory. Conrad's
notes gives a more down-to-earth exposition.
hypercovering, of
which a
cohomological descent is a
generalization Conrad n.d., Lemma...
-
finer hypercoverings (which is
technically accomplished by
working with the pro-object in
simplicial sets
determined by
taking all
hypercoverings), the...
-
simplicial presheaf F on a site is
called a
stack if, for any X and any
hypercovering H →X, the
canonical map F ( X ) →
holim F ( H n ) {\displaystyle F(X)\to...
