{"id":3265,"date":"2013-06-28T02:44:38","date_gmt":"2013-06-28T02:44:38","guid":{"rendered":"http:\/\/math.columbia.edu\/~dejong\/wordpress\/?p=3265"},"modified":"2013-06-28T02:53:28","modified_gmt":"2013-06-28T02:53:28","slug":"update-22","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/?p=3265","title":{"rendered":"Update"},"content":{"rendered":"

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

    \n
  1. universal property of blowing up (schemes) Tag 0806<\/a><\/li>\n
  2. admissible blowups (schemes) Tag 080J<\/a><\/li>\n
  3. strict transform (schemes) Tag 080C<\/a><\/li>\n
  4. a section on fitting ideals (algebra) Tag 07Z6<\/a><\/li>\n
  5. flattening by blowing up (schemes) Tag 080X<\/a><\/li>\n
  6. proper modifications can be dominated by blowups (schemes) Tag 081T<\/a><\/li>\n
  7. relative spectrum (spaces) Tag 03WD<\/a><\/li>\n
  8. scheme theoretic closure (spaces) Tag 0831<\/a><\/li>\n
  9. effective Cartier divisors (spaces) Tag 083A<\/a><\/li>\n
  10. relative Proj (spaces) Tag 0848<\/a><\/li>\n
  11. blowing up (spaces) Tag 085P<\/a><\/li>\n
  12. strict transforms (spaces) Tag 0861<\/a><\/li>\n
  13. admissible blowups (spaces) Tag 086A<\/a><\/li>\n
  14. generalities on limits (spaces) Tag 07SB<\/a><\/li>\n
  15. flattening by blowups (spaces) Tag 087A<\/a><\/li>\n
  16. David Rydh’s result that a decent space has a dense\u00a0open subscheme\u00a0Tag 086U<\/a><\/li>\n
  17. QCoh is Grothendieck (spaces and stacks)\u00a0Tag 077V<\/a>\u00a0Tag 0781<\/a><\/li>\n
  18. proper modifications can be dominated by blowups (spaces)\u00a0Tag 087G<\/a><\/li>\n
  19. multiple versions of Chow’s lemma (spaces)\u00a0Tag 089J<\/a>\u00a0Tag 088U<\/a>\u00a0Tag 089L<\/a>\u00a0Tag 089M<\/a><\/li>\n
  20. David Rydh’s result that a locally separated\u00a0algebraic space is decent\u00a0Tag 088J<\/a><\/li>\n
  21. Grothendieck existence theorem (schemes)\u00a0Tag 087V<\/a>\u00a0Tag 0886<\/a><\/li>\n
  22. Grothendieck algebraization theorem (schemes)\u00a0Tag 089A<\/a><\/li>\n
  23. proper pushforward preserves coherence (spaces)\u00a0Tag 08AP<\/a><\/li>\n
  24. theorem on formal functions (spaces)\u00a0Tag 08AU<\/a><\/li>\n
  25. Grothendieck existence theorem (spaces)\u00a0Tag 08BE<\/a>\u00a0Tag 08BF<\/a><\/li>\n
  26. a little bit about m-regularity\u00a0Tag 08A2<\/a><\/li>\n
  27. connected spaces are nonempty (thanks to Burt)\u00a0Tag 004S<\/a><\/li>\n
  28. decent group space over field is separated\u00a0Tag 08BH<\/a><\/li>\n
  29. derived Mayer-Vietoris (ringed spaces)\u00a0Tag 08BR<\/a><\/li>\n
  30. derived categories of modules (schemes)\u00a0Tag 08CV<\/a><\/li>\n
  31. D(QCoh(O_X) = D_{QCoh}(O_X) for X quasi-compact with\u00a0affine diagonal (schemes)\u00a0Tag 08DB<\/a><\/li>\n
  32. Lipman and Neeman’s result on approximation by perfect\u00a0complexes (schemes)\u00a0Tag 08ES<\/a><\/li>\n
  33. derived categories of modules (spaces),\u00a0Tag 08EZ<\/a><\/li>\n
  34. Induction principle for quasi-compact and quasi-separated\u00a0algebraic spaces using distinguished squares (this is really fun!)\u00a0Tag 08GL<\/a><\/li>\n
  35. derived Mayer-Vietoris using distinguished squares\u00a0Tag 08GS<\/a><\/li>\n
  36. D(QCoh(O_X) = D_{QCoh}(O_X) for X quasi-compact with\u00a0affine diagonal (spaces)\u00a0Tag 08H1<\/a><\/li>\n
  37. approximation by perfect complexes (spaces)\u00a0Tag 08HP<\/a><\/li>\n
  38. bunch of improvements to the bibliography\u00a0bibliography<\/a><\/li>\n
  39. being projective is not local on the base\u00a0Tag 08J0<\/a><\/li>\n
  40. descent data for schemes need not be effective, even for\u00a0a projective morphism\u00a0Tag 08KE<\/a><\/li>\n
  41. base change for Rf_*RHom(E, G) (schemes)\u00a0Tag 08IC<\/a><\/li>\n
  42. base change for Rf_*RHom(E, G) (spaces)\u00a0Tag 08JM<\/a><\/li>\n
  43. the Hom<\/i> functor\u00a0Tag 08JS<\/a><\/li>\n
  44. the stack of coherent sheaves\u00a0Tag 08WC<\/a><\/li>\n
  45. deformation theory: rings, modules, ringed spaces,\u00a0sheaves of modules on ringed spaces, ringed topoi,\u00a0sheaves of modules on ringed topoi\u00a0Tag 08KX<\/a><\/li>\n
  46. subtopoi\u00a0Tag 08LT<\/a><\/li>\n
  47. standard simplicial resolutions\u00a0Tag 08N8<\/a><\/li>\n
  48. cotangent complex\u00a0Tag 08P6<\/a><\/li>\n
  49. snake lemma now has a proof without picking elements\u00a0Tag 010H<\/a><\/li>\n
  50. constructing polynomial resolutions\u00a0Tag 08PX<\/a><\/li>\n
  51. (trivial) Kan fibrations\u00a0Tag 08NK<\/a>\u00a0Tag 08NT<\/a><\/li>\n
  52. Quillen’s spectral sequence\u00a0Tag 08RF<\/a><\/li>\n
  53. cotangent complex and obstructions (algebra)\u00a0Tag 08SP<\/a><\/li>\n
  54. cotangent complex and obstructions (ringed spaces)\u00a0Tag 08UZ<\/a><\/li>\n
  55. cotangent complex and obstructions (ringed topoi)\u00a0Tag 08V5<\/a><\/li>\n
  56. fixed an error in Artin’s axioms point out by David Rydh\u00a02ccbbe3087e4dc2b1df2193c81ede7486931424c<\/a><\/li>\n
  57. skeleton chapter on dualizing complexes (algebra)\u00a0Tag 08XH<\/a><\/li>\n
  58. descent for universally injective morphisms (thanks to Kiran Kedlaya)\u00a0Tag 08WE<\/a><\/li>\n<\/ol>\n

    This brings us up to May 1 of this year. At that point I started to work on a chapter on pro-\\’etale cohomology<\/a>, in order to advertise work by Bhargav Bhatt and Peter Scholze in some lectures in Stockholm (KTH). The authors graciously send me a copy of their (for the moment) unfinished manuscript. The chapter covers only a small part of their material, leading up to the definition of constructible complexes and the proper base change theorem. All mistakes are mine. I’ve tried to put most of the background material in other chapters. As is usual for the Stacks project, whenever you try to add something new you are forced to add a lot of background material to go along with it. Here is a list of some of the things we added.<\/p>\n

      \n
    1. pro-\\’etale cohomology (schemes)\u00a0Tag 0966<\/a><\/li>\n
    2. Gleason’s theorem on extremally disconnected spaces\u00a0(I strongly recommend the original paper)\u00a0Tag 08YH<\/a><\/li>\n
    3. Hochster’s spectral spaces\u00a0(I strongly recommend the original paper)\u00a0Tag 08YF<\/a><\/li>\n
    4. Stone Cech compactification\u00a0Tag 0908<\/a><\/li>\n
    5. Olivier’s theorem on absolutely flat extensions of\u00a0strictly henselian rings\u00a0(I strongly recommend the original paper)\u00a0Tag 092Z<\/a><\/li>\n
    6. weakly \\’etale morphisms (schemes)\u00a0Tag 094N<\/a><\/li>\n
    7. derived completion (algebra; I’ve tried to give\u00a0some references but I’d love to know more about the history\u00a0of this topic)\u00a0Tag 091N<\/a><\/li>\n
    8. constructible sheaves (etale)\u00a0Tag 05BE<\/a>\u00a0Tag 095M<\/a><\/li>\n
    9. derived completion (ringed topoi)\u00a0Tag 0995<\/a>\u00a0Tag 099L<\/a>\u00a0Tag 099P<\/a><\/li>\n
    10. derived category D_c (etale)\u00a0Tag 095V<\/a><\/li>\n<\/ol>\n

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

      Since the last update we have added the following material: universal property of blowing up (schemes) Tag 0806 admissible blowups (schemes) Tag 080J strict transform (schemes) Tag 080C a section on fitting ideals (algebra) Tag 07Z6 flattening by blowing up … 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-3265","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\/3265","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=3265"}],"version-history":[{"count":7,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3265\/revisions"}],"predecessor-version":[{"id":3272,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/3265\/revisions\/3272"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3265"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3265"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~dejong\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}