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Chapter Page 1 INTRODUCTION
THE SPECTRUM OF A COMMUTATIVE RING
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A-module abelian groups affine open sets affine scheme affine varieties algebraic geometry algebraic varieties axiom basic open sets canonical divisor ch(E Chapter Chern classes Chern roots coefficients coherent sheaf commutative ring coordinate ring CP(U Cq(U defined diagram embedding epimorphism exact sequence exists finite type follows gives rise Grothendieck hence homo HP(U HP(X Hq(U Hq(X identity element integer intersection isomorphic k-algebra k-variety kernel left exact Lemma Module homomorphism morphism of preschemes nilpotent elements open covering open neighbourhood open set open sets D(f polynomial presheaf prime ideal projective variety Proof Proposition Q is coherent quasi-coherent quasi-compact rational function regular map restriction homomorphisms Riemann-Roch theorem ring homomorphism ringed space s e 3(U S-prescheme sheaf associated sheaf of rings sheaves Spec Spec(A stalks subvarieties surjective tensor product topological space vector bundle Zariski topology zero