Beyond varieties — discover how Grothendieck's schemes reveal geometric structure invisible to classical algebraic geometry through 23 interactive demonstrations covering Spec, sheaves, gluing, fiber products, and sheaf cohomology.
See also: Algebraic Geometry for classical varieties, elliptic curves, and the algebra–geometry dictionary.
Every commutative ring has a geometry — Spec(Z), Spec(k[x]), and the points you never knew you were missing
A topology where open sets are huge and closed sets are rare — and why that's exactly right
Local data that glues — how sheaves encode "functions defined on open sets" consistently
The triple (Spec R, O, R) — assembling topology, sheaf, and ring into a geometric object
Building global schemes from affine pieces — the projective line P¹ and beyond
Maps between schemes, base change, and families of geometric objects
Reduced, irreducible, integral, separated, proper — the adjectives of scheme theory
Counting global sections, measuring obstructions, and the most powerful theorem in algebraic geometry