Grothendieck topology
Topología de Grothendieck
- Date
- c. 1962 · confidence low
- Place
- Bures-sur-Yvette, France
- Credited to
- Alexander Grothendieck
- Field
- Knowledge & symbols
What it is
A Grothendieck topology is a structure defined on a category that makes its objects behave like the open sets of a topological space, allowing sheaves and their cohomology to be defined in a general categorical setting (a 'site'). It was introduced by mathematician Alexander Grothendieck in the early 1960s, within algebraic geometry.
What it led to
- Foundation of étale cohomology used to prove the Weil conjectures
- Generalization of the notion of topological space in modern algebraic geometry
- Basis of the notion of topos in category theory