Pathway X

SpecRing theory and algebraic geometry

Rings, ideals, quotients — then Spec, and a cubic that is a group.

1. 01SpecThe spectrum of a ring is its prime ideals, with closed sets V(I) = {p : I ⊆ p}.4 min
2. 02Ideals and quotientsAn ideal absorbs multiplication from the ring. The quotient R/I is the ring as seen from I.4 min
3. 03Elliptic curvesA smooth cubic y² = x³ + ax + b. The chord-and-tangent law makes its points a group.4 min