higher geometry / derived geometry
higher topos theory
higher algebra
geometric little (∞,1)-toposes
structured (∞,1)-topos
geometry (for structured (∞,1)-toposes)
generalized scheme
geometric big (∞,1)-toposes
function algebras on ∞-stacks
loop space object, free loop space object
fundamental ∞-groupoid in a locally ∞-connected (∞,1)-topos / of a locally ∞-connected (∞,1)-topos
derived algebraic geometry
étale (∞,1)-site, Hochschild cohomology of dg-algebras
dg-geometry
schematic homotopy type
derived noncommutative geometry
derived smooth geometry
differential geometry, differential topology
derived smooth manifold, dg-manifold
smooth ∞-groupoid, ∞-Lie algebroid
higher symplectic geometry
higher Klein geometry
higher Cartan geometry
Isbell duality
Jones' theorem, Deligne-Kontsevich conjecture
Tannaka duality for geometric stacks
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A notion of (Berkovich) analytic space in the context of noncommutative geometry.
p-adic number
non-archimedean field