The projective spectrum as a distributive lattice
Résumé
We construct a distributive lattice whose prime filters correspond to the homogeneous prime ideals of a graded commutative ring. This is the prime example of a non-affine scheme in a point-free context, and the model case of a fairly general glueing method for distributive lattices. We furthermore prove the projective form of the formal Hilbert Nullstellensatz.