Algebraic geometry II - schemes and sheaves

In lecture 9, we covered the following topics:

-if S is an N-graded ring, Proj(S) is a scheme;

-regular local rings;

-geometric interpretation of Nakayama's lemma as an algebraic version of the implicit function theorem;

-(locally) Noetherian schemes;

-Zariski (co)tangent space at a point;

-technical lemmas towards the Jacobian criterion.