{"id":4019,"date":"2015-06-16T20:07:11","date_gmt":"2015-06-16T20:07:11","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=4019"},"modified":"2015-06-16T20:07:11","modified_gmt":"2015-06-16T20:07:11","slug":"update-24","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=4019","title":{"rendered":"Update"},"content":{"rendered":"

Since the last update of October 2014<\/a> we have added the following material:<\/p>\n

    \n
  1. Structure modules over PIDs following Warfield Tag 0ASL<\/a><\/li>\n
  2. Correct proof of Lemma Tag 05U9<\/a> thanks to Ofer Gabber<\/li>\n
  3. A flat ring map which is not a directed colimit of flat finitely presented ring maps Tag 0ATE<\/a><\/li>\n
  4. Glueing dualizing complexes Tag 0AU5<\/a><\/li>\n
  5. Trace maps Tag 0AWG<\/a><\/li>\n
  6. Duality for a finite morphism Tag 0AWZ<\/a><\/li>\n
  7. Grauert-Riemenschneider for surfaces Tag 0AX7<\/a><\/li>\n
  8. Torsion free modules Tag 0AVQ<\/a><\/li>\n
  9. Reflexive modules Tag 0AVT<\/a><\/li>\n
  10. Finiteness theorem for f_* Tag 0AW7<\/a><\/li>\n
  11. Fix definition of depth (thanks to Burt) Tag 00LE<\/a> and Tag 0AVY<\/a><\/li>\n
  12. Characterizing universally catenary rings Tag 0AW1<\/a><\/li>\n
  13. Improved section on Jacobson spaces thanks to Juan Pablo Acosta Lopez Tag 005T<\/a><\/li>\n
  14. Faithfully flat descent of ML modules thanks to Juan Pablo Acosta Lopez Tag 05A5<\/a><\/li>\n
  15. Improvements to the chapter on Chow homology discussed here<\/a><\/li>\n
  16. Degrees of vector bundles on curves Tag 0AYQ<\/a><\/li>\n
  17. Degrees of zero cycles Tag 0AZ0<\/a> and how this relates to degrees of vector bundles and with numerical intersections<\/li>\n
  18. Quotient by category of torsion modules thanks to Ingo Blchschmidt Tag 0B0J<\/a><\/li>\n
  19. New chapter on intersection theory discussed here<\/a><\/li>\n
  20. Example of different colimit topologies Tag 0B2Y<\/a><\/li>\n
  21. Section on topological groups, rings, modules Tag 0B1Y<\/a><\/li>\n
  22. Section on tangent spaces Tag 0B28<\/a><\/li>\n
  23. A bunch of material on (quasi-)projectivity, for example Tag 0B41<\/a> and Tag 0B44<\/a><\/li>\n
  24. Glueing in a modification Tag 0B3W<\/a> at a point of a scheme<\/li>\n
  25. Improved material on sober spaces thanks to Fred Rohrer Tag 004U<\/a><\/li>\n
  26. Riemann-Roch and duality for curves Tag 0B5B<\/a><\/li>\n
  27. Fix idiotic mistake about graded projective modules, thanks to Rishi Vyas read his explanation on github<\/a><\/li>\n
  28. Base change map in duality Tag 0AA5<\/a> is often an isomorphism (Tag 0AA8<\/a>) and commutes with base change Tag 0AWG<\/a><\/li>\n
  29. Bunch of changes thanks to Darij Grinberg<\/a><\/li>\n
  30. Material on group schemes over fields Tag 047J<\/a><\/li>\n
  31. Material on (locally) algebraic group schemes over fields Tag 0BF6<\/a><\/li>\n
  32. Thickenings of quasi-affine schemes are quasi-affine Tag 0B7L<\/a><\/li>\n
  33. Minimal closed subspaces which aren’t schemes Tag 0B7X<\/a><\/li>\n
  34. Monomorphisms of algebraic spaces Tag 0B89<\/a><\/li>\n
  35. Change of base field and schematic locus Tag 0B82<\/a><\/li>\n
  36. Separated group algebraic spaces over fields are schemes Tag 0B8G<\/a><\/li>\n
  37. Picard scheme of smooth projective curves over algebraically closed fields Tag 0B92<\/a><\/li>\n
  38. Improved discussion of invertible modules… (too ashamed to put a link here)<\/li>\n
  39. Jacobson algebraic spaces Tag 0BA2<\/a><\/li>\n
  40. Nagata spaces Tag 0BAT<\/a><\/li>\n
  41. For an algebraic space: locally Noetherian + decent => quasi-separated Tag 0BB6<\/a><\/li>\n
  42. Various improvements on rational and birational maps Tag 01RR<\/a>, Tag 01RN<\/a>, and Tag 0BAJ<\/a><\/li>\n
  43. Dimension formula for algebraic spaces Tag 0BAW<\/a><\/li>\n
  44. Generically finite morphisms of algebraic spaces Tag 0BBA<\/a><\/li>\n
  45. Birational morphisms of algebraic spaces Tag 0ACU<\/a><\/li>\n
  46. Elementary etale neighbourhoods on algebraic spaces Tag 03IG<\/a><\/li>\n
  47. Complements of affine opens have codimension 1 Tag 0BCQ<\/a><\/li>\n
  48. Norms of invertible modules Tag 0BCX<\/a> which allows us to descend ample invertible modules<\/li>\n
  49. Descending (quasi-)projectivity through field extensions Tag 0BDB<\/a><\/li>\n
  50. Section on splitting complexes Tag 0BCF<\/a> for better handling of local structure of perfect complexes<\/li>\n
  51. Section on stably free modules Tag 0BC2<\/a><\/li>\n
  52. Jumping loci for perfect complexes on schemes Tag 0BDH<\/a><\/li>\n
  53. Applications of cohomology and base change Tag 0BDM<\/a><\/li>\n
  54. Theorem of the cube Tag 0BEZ<\/a><\/li>\n
  55. Weil divisors on locally Noetherian schemes Tag 0BE0<\/a><\/li>\n
  56. The Weil divisor class associated to an invertible module Tag 02SE<\/a><\/li>\n
  57. K\\”unneth formula for schemes over a field Tag 0BEC<\/a><\/li>\n
  58. Algebraic group schemes are quasi-projective Tag 0BF7<\/a><\/li>\n
  59. Numerical intersections Tag 0BEL<\/a><\/li>\n
  60. Section on abelian varieties Tag 0BF9<\/a> containing just enough for our use later<\/li>\n
  61. Tried to improve the exposition of convergence for spectral sequences using terminology mostly as in Weibel; still very far from perfect<\/li>\n
  62. Long overdue characterization of algebraic spaces Tag 0BGQ<\/a><\/li>\n
  63. Chapters on resolution of surface singularities one for schemes<\/a> and one for algebraic spaces<\/a>\n<\/ol>\n

    Enjoy!<\/p>\n","protected":false},"excerpt":{"rendered":"

    Since the last update of October 2014 we have added the following material: Structure modules over PIDs following Warfield Tag 0ASL Correct proof of Lemma Tag 05U9 thanks to Ofer Gabber A flat ring map which is not a directed … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-4019","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/4019","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4019"}],"version-history":[{"count":2,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/4019\/revisions"}],"predecessor-version":[{"id":4021,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/4019\/revisions\/4021"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4019"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}