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...Mit opencourseware http ocw edu algebraic geometry spring for information about citing these materials or our terms of use visit k s kedlaya problem set due friday march in class please submit exactly eleven the following exercises including all marked required note that hartshorne are now coming from both chapters ii and iii read closely eisenbud harris let a b be homomorphism rings prove is faithfully at over sense commutative algebra i e any module m adjunction map modules injective if only spec surjective morphism schemes faithful descent quasicoherent sheaves as follows f ring induced by idb denote multiplication given equipped with datum recover underlying forming between ane two embeddings isomorphism construct submodule n consisting those which show an hint since we may replace respectively then c reducing to case deduce galois without using theorem properties can checked after quasicompact base change universally closed separated proper quasinite it nite type has bres inverse ...