Martin Orr's Blog

Algebraic geometry posts

Nullstellenstatz

• Proof of the Nullstellensatz

Functor of points

• The functor of points of an affine variety
• Functors, affine varieties and Yoneda
• Affine k-schemes
• Morphisms and functors of points
• Functors of points and base ring
• Functor of points of non-affine schemes
• Galois ascent for functors of points
• Galois descent for morphisms of functors of points

Algebraic tori

• Algebraic tori
• Hopf algebras and algebraic groups
• Character groups of algebraic tori
• Representations of algebraic tori

Hensel's lemma

• Hensel's lemma and algebraic functions
• Ordinary multiple points