Some (delphic?) notes on trouble spots on homework problems. H.p means problem p on homework set H.

• 1.2 A complete answer accounts for the fact that different polynomials can generate the same maximal ideal.
• 2.1 This requires the Nullstellensatz. Where?
• 2.5 Make sure you understand the definition of an open subcover. How can one reduce to considering only coverings by distinguished opens?
• 3.1 Unless explicitly stated, we are always working over an algebraically closed field.
• 3.2 You may need to use a different representative for the function at different points; k[X] need not be a UFD.
• 3.3b Figure out if you're thinking of &phi^* as a map from k[W] to k[V] or from k[w₁, ..., w_n] to k[V].