A differentiable stack X may be equipped with Grothendieck topology in a certain way (see the reference).
André Weil's famous Weil conjectures proposed that certain properties of equations with integral coefficients should be understood as geometric properties of the algebraic variety that they define.
Weak topology | Trivial topology | Pointless topology | Initial topology | Grothendieck topology | differential topology | Boundary (topology) |
The idea of a Grothendieck topology (also known as a site) has been characterised by John Tate as a bold pun on the two senses of Riemann surface.