Definition of Hypercoverings. Meaning of Hypercoverings. Synonyms of Hypercoverings

- cover U 2 {\displaystyle {\mathcal {U}}_{2}} , and so on, iteratively. Hypercoverings have a central role in étale homotopy and other areas where homotopy...
- among them the Čech nerve of a cover, which in turn is generalised by hypercoverings. It captures many of the interesting topological properties in an algorithmic...
- Čech cohomology and sheaf cohomology is a motivation for the use of hypercoverings: these are more general objects than the Čech nerve N X U : ⋯ → U ×...
- cohomology groups. To get around this, Jean-Louis Verdier developed hypercoverings. Hypercoverings not only give the correct higher cohomology groups but also...
- French Alma mater University of Paris Known for Verdier duality Verdier hypercovering theorem Artin–Verdier duality Serre–Grothendieck–Verdier duality Derived...
- finer hypercoverings (which is technically accomplished by working with the pro-object in simplicial sets determined by taking all hypercoverings), the...
- has fiber products. The coskeleton is needed to define the concept of hypercovering in homotopical algebra and algebraic geometry. Peter McMullen, Egon...
- 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...
- 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...