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File: Geometry Pdf 168132 | 632hmwk
math 632 algebraic geometry 2 scheme theory homework assigments professorkarene smith please turn in your problems by the stated dates by thursday january 17 shafarevich vol 2 chapter 5 1 ...

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                         MATH 632: ALGEBRAIC GEOMETRY 2
                                   SCHEME THEORY
                               HOMEWORK ASSIGMENTS
                                 PROFESSORKARENE.SMITH
              Please turn in your problems by the stated dates.
            By Thursday January 17: Shafarevich Vol 2 Chapter 5 §1: 1, 2, 3, 5, 6 [Correc-
            tions: In 2, the decomposition is into closed sets, which may not be proper. In 5,
            take E to be an ideal, not just a set.]
            By Tuesday January 22: Hartshorne: II §1: 1.2, 1.5, 1.10, 1.12, 1.14. [For these,
            use Hartshorne’s definition of surjective and injective maps of presheaves.]
            By Thursday January 24:   Hartshorne: II §1: 1.3, 1.6, 1.9, 1.15, 1.17 [Note:
            Hartshorne’s sheaves are all sheaves of abelian groups.]
            By Tuesday January 29:  Hartshorne: II §1: 1.16, 1.18, 1.21, 1.22 [Note: The
            notation Hom(F,G) in 18 denotes the set of homomorphism between the named
            sheaves. This is not the same thing as in problem 1.15, which is a sheaf on X, not
            a set. Note the different fonts.]
            By Thursday January 31: Hartshorne II §2: 2.1, 2.2, 2.3, 2.4, 2.7
            By Tuesday Feb 5: Hartshorne II §2: 2.8, 2.9, 2.11, 2.12,
            By Thursday Feb 7: Hartshorne II §2: 2.14, 2.16, 2.18
            By Tuesday Feb 12: Hartshorne II §3: 3.1, 3.4, 3.6, 3.7, 3.8
            By Thursday Feb 14: Hartshorne II §3: 3.9, 3.10, 3.12, 3.13, 3.21
            By Tuesday Feb 19: Hartshorne II §5: 5.1, 5.3, 5.5, 5.6
              But do not turn them in to David Speyer; wait for my return and turn them in
            2/26.
            By Thursday Feb 21: Hartshorne II §5: 5.7, 5.8, 5.9
              But do not turn them in to David Speyer; wait for my return and turn them in
            2/26.
            By Tuesday Feb 26: Hartshorne II §4: 4.1, 4.3, 4.4, 4.6,
            By Thursday Feb 28: Hartshorne II §4: 4.5, 4.8
                                            1
                   2                       PROFESSORKARENE.SMITH
                   By Thursday Feb 28: Hartshorne II §4: 4.5, 4.8
                   BREAK!
                   By Tuesday March 12 : Hartshorne II §5: 5.10, 5.11, 5.12,
                   By Thursday March 14: Hartshorne II §5: 5.13, 5.14,
                   By Tuesday March 19: Hartshorne II §5: 5.17, 5.18.
                   By Thursday March 21: Hartshorne II §6: 6.2ab (note typo in a, the letter i is
                   used in two different contexts), 6.5 abc. Complete QUIZ 4 if you have not already!
                                                                                   4 3   3  4
                   ByTuesdayMarch26: HartshorneII§7: 7.1,7.2,7.3,ShowthatSpeck[s ,s t,st ,t ]
                                                            2 2                   2 2
                   satisfies (∗) but is not normal, and that div (s t ) is effective although s t is not
                   regular.
                   By Thursday April 2: Hartshorne II §7: 7.5, 7.7
                   By Tuesday April 2: 7.5, 7.7
                   ByThursdayApril4: Proveallthestatementsregardingthethreedifferentmaps
                   from the blow-up of P2 at a point to different projective spaces discussed in class on
                   March 28. (See the Daily Update.)
                   By Tuesday April 9:   Hartshorne III 2.1a, 2.2, 2.7 (Hint: both Q and Q/Z are
                   injective Z-modules.). If you want more, try also 2.3, 2.4. If your homological algebra
                   is weak, study instead Dummit and Foote’s chapter 17, and do some of the exercises
                   there.
                   ByThursday April 11: Hartshorne III 3.1, 3.2, 3.3. If your commutative algebra
                   is strong (eg, you know what “depth” means), you might also like 3.4 and 3.5.
                   By Tuesday April 16: Hartshorne III 4.1, 4.3, 4.7
                   By Thursday April 18:    Hartshorne III 5.1, 5.2, 5.5 [For folks cruising along:
                   5.3 and 5.6 are interesting and important, and not too difficult if you are following
                   everything.]
                   By Tuesday April 23: Hartshorne IV: 1.1, 1.2, 1.3, 1.4, 1.5,
                   By April 29, for those A+ students who want more: Hartshorne IV: 1.6, 1.7, 3.1.
                   You are now in a pretty good position to read Chapters IV and V of Hartshorne. If
                   you plan to continue in algebraic geometry, this is a good summer plan. [You can go
                   back to II and III as needed, but IV and V are very classical and don’t use most of
                   the fancy stuff from II and III.]
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...Math algebraic geometry scheme theory homework assigments professorkarene smith please turn in your problems by the stated dates thursday january shafarevich vol chapter tuesday hartshorne ii feb but do not them to david speyer wait for my return and break march ab note typo a letter i is used two dierent contexts abc complete quiz if you have already bytuesdaymarch hartshorneii showthatspeck satises normal that div s t eective although regular april bythursdayapril proveallthestatementsregardingthethreedierentmaps from blow up of p at point projective spaces discussed class on see daily update iii hint both q z are injective modules want more try also homological algebra weak study instead dummit foote some exercises there bythursday commutative strong eg know what depth means might like iv those students who now pretty good position read chapters v plan continue this summer...

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