commit ef18f27eaca526453471d5d933acc81a58d18a13 Author: Aise Johan de Jong Date: Wed May 16 14:15:42 2012 -0400 Improved statement of absolute Noetherian approximation The argument of absolute Noetherian approximation shows a little bit more. We explicitly state what it gives us as we can use it to prove an interesting result for algebraic spaces. decent-spaces.tex | 2 +- limits.tex | 171 +++++++++++++++++++++++++++++++++---------------- spaces-properties.tex | 2 +- 3 files changed, 117 insertions(+), 58 deletions(-) commit 7e0556525c8008152acc603ad16540bf5b110cac Author: Aise Johan de Jong Date: Wed May 16 12:01:51 2012 -0400 Improve chapter on decent spaces A collection of things: get rid of the very reasonable material. This is possible because we can now prove everything for reasoble spaces which was previously only proved for very reasonable spaces. decent-spaces.tex | 497 +++++++++++++++++++++++++------------------------ more-morphisms.tex | 14 ++ obsolete.tex | 126 +++++++++++++ properties.tex | 26 ++- spaces-properties.tex | 20 +- tags/tags | 30 ++-- 6 files changed, 441 insertions(+), 272 deletions(-) commit 5158ffdae7dec1b6a9729dc8e02c26089b52e922 Author: Aise Johan de Jong Date: Tue May 15 20:53:09 2012 -0400 Stratify by degree fibre This works well for flat, lfp, quasi-finite morphisms. etale-cohomology.tex | 5 ++- more-morphisms.tex | 144 +++++++++++++++++++++++++++++++++++++++++++++++--- 2 files changed, 140 insertions(+), 9 deletions(-) commit 1105aae1ecb2ab39a2cec8b0599954cedf244b59 Author: Aise Johan de Jong Date: Tue May 15 11:23:05 2012 -0400 Quasi-projective over a qcqs base is open in projective morphisms.tex | 161 ++++++++++++++++++++++++++++++++++++++++++++++++++------ 1 files changed, 143 insertions(+), 18 deletions(-) commit f70269739955b8544aaee7bab7c998b8659b2279 Author: Aise Johan de Jong Date: Tue May 15 10:19:59 2012 -0400 Quotients which are schemes Just a clear statement of what we've already proved. flat.tex | 2 +- groupoids.tex | 38 ++++++++++++++++++-- spaces-properties.tex | 94 ++++++++++++++++++++++++++++++++++++++++++++++--- spaces.tex | 7 +++- 4 files changed, 129 insertions(+), 12 deletions(-) commit c54239bfe0089836ab87f20a8dbfffc2c164622d Author: Aise Johan de Jong Date: Sun May 13 18:04:44 2012 -0400 Small changes more-morphisms.tex | 6 +++--- spaces-cohomology.tex | 4 ++-- spaces-more-morphisms.tex | 7 +++---- spaces-morphisms.tex | 4 ++-- 4 files changed, 10 insertions(+), 11 deletions(-) commit bc346d40ce9c144ec40ed7a4541a430ad6a9e4e5 Author: Aise Johan de Jong Date: Sat May 12 21:06:02 2012 -0400 'pull back' ----> 'pullback' This is a bit more tricky as we sometimes use the pull in 'pull back' as a verb. algebra.tex | 2 +- chow.tex | 6 +++--- constructions.tex | 2 +- crystalline.tex | 2 +- descent.tex | 2 +- flat.tex | 6 +++--- homology.tex | 4 ++-- modules.tex | 4 ++-- sheaves.tex | 2 +- sites.tex | 2 +- spaces-descent.tex | 2 +- spaces-groupoids.tex | 6 +++--- stacks.tex | 4 ++-- topologies.tex | 10 +++++----- 14 files changed, 27 insertions(+), 27 deletions(-) commit 490b569db93213b47ddac61fe661d974ea87d2e1 Author: Aise Johan de Jong Date: Sat May 12 20:53:18 2012 -0400 'push forward' ---> 'pushforward' chow.tex | 2 +- crystalline.tex | 4 ++-- schemes.tex | 2 +- sheaves.tex | 2 +- sites.tex | 2 +- topologies.tex | 6 +++--- 6 files changed, 9 insertions(+), 9 deletions(-) commit a17cc93544fa47b69ee331503c6f796efcbf4827 Author: Aise Johan de Jong Date: Sat May 12 20:50:00 2012 -0400 'push out' ---> 'pushout' categories.tex | 14 +++++++------- cohomology.tex | 4 ++-- crystalline.tex | 4 ++-- examples.tex | 2 +- exercises.tex | 2 +- homology.tex | 6 +++--- limits.tex | 2 +- more-morphisms.tex | 20 ++++++++++---------- simplicial.tex | 22 +++++++++++----------- sites-cohomology.tex | 6 +++--- spaces-more-morphisms.tex | 6 +++--- 11 files changed, 44 insertions(+), 44 deletions(-) commit 55e6b4ceca6ac10c222fced130cba00fd94c0e3d Author: Aise Johan de Jong Date: Thu May 10 17:17:06 2012 -0400 Case of pushout schemes which also works for algebraic spaces Fun little lemma about when this kind of thing works for colimits of schemes. categories.tex | 2 +- more-morphisms.tex | 6 ++- spaces-more-morphisms.tex | 76 ++++++++++++++++++++++++++++++++++++++++++++- 3 files changed, 80 insertions(+), 4 deletions(-) commit 3f35f360cb9ca1c4deb73a02a9f250d6ba1c1520 Author: Aise Johan de Jong Date: Thu May 10 14:48:11 2012 -0400 zerodivisor and nonzerodivisor Seems better this way. algebra.tex | 194 ++++++++++++++++++++++++++-------------------------- chow.tex | 36 +++++----- divisors.tex | 96 +++++++++++++------------- examples.tex | 4 +- exercises.tex | 34 +++++----- flat.tex | 14 ++-- more-algebra.tex | 8 +- more-groupoids.tex | 2 +- more-morphisms.tex | 22 +++--- morphisms.tex | 4 +- smoothing.tex | 2 +- 11 files changed, 208 insertions(+), 208 deletions(-) commit 1028202cbedbd79345d0899b76e1e7dc732b6360 Author: Aise Johan de Jong Date: Thu May 10 08:54:28 2012 -0400 Two typos Thanks to Yuhao Huang algebra.tex | 4 ++-- 1 files changed, 2 insertions(+), 2 deletions(-) commit c97eb5fadc98013b1588fb34b2ecf43d2309c2e3 Author: Aise Johan de Jong Date: Wed May 9 21:27:05 2012 -0400 Skeleton section on push outs in the category of algebraic spaces spaces-more-morphisms.tex | 18 ++++++++++++++++++ 1 files changed, 18 insertions(+), 0 deletions(-) commit 818daac28378cf99d1fc48a9f6d734de906c1c5f Author: Aise Johan de Jong Date: Wed May 9 21:24:35 2012 -0400 Push outs and relative schemes This commit contains a somewhat tricky result. Namely if Y' is the pushout of an affine morphism X ---> Y by a thickening X ---> X' then the category of schemes flat over Y' is equivalent to the category of triples (V, U', \varphi) where V/Y and U'/X' are flat and \varphi is an isomorphism between their base changes to X. At least I don't think this is formal. Do you? more-morphisms.tex | 230 +++++++++++++++++++++++++++++++++++++++++++++++++++- 1 files changed, 229 insertions(+), 1 deletions(-) commit 9a07b1f06b289051d57e678d23e89939a5ceb287 Author: Aise Johan de Jong Date: Wed May 9 21:22:36 2012 -0400 An application of criterion flatness per fibre Namely, if S ---> S' is a map of finitely presented algebras over R and I is a locally nilpotent ideal of R such that S/IS ---> S'/IS' is an isomorphism, and S' is flat over R, then S ---> S' is an isomorphism. algebra.tex | 55 +++++++++++++++++++++++++++++++++++++++++++++++++++---- 1 files changed, 51 insertions(+), 4 deletions(-) commit a93a362ed973fa08f8044ae2ffc6ea8cfd4ba0eb Author: Aise Johan de Jong Date: Wed May 9 21:21:45 2012 -0400 Adjoint functors A bit more about them. categories.tex | 46 ++++++++++++++++++++++++++++++++++++++++++---- 1 files changed, 42 insertions(+), 4 deletions(-) commit 7c394868827a5a4e6b7884c87aaa545d369a06ec Author: Aise Johan de Jong Date: Wed May 9 09:04:40 2012 -0400 Case of pushout schemes One morphism is affine and the other is a thickening. more-morphisms.tex | 91 ++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 files changed, 91 insertions(+), 0 deletions(-) commit 04e80945da27b83912449c1b5a6b38f202bffb9a Author: Aise Johan de Jong Date: Tue May 8 17:16:50 2012 -0400 Fix two typos Thanks to David Zureick-Brown CONTRIBUTORS | 1 + guide.tex | 9 +++++---- sites.tex | 2 +- 3 files changed, 7 insertions(+), 5 deletions(-) commit 23d824d77d9f9b9c2263f04704b3957a8a4c29bb Author: Aise Johan de Jong Date: Mon May 7 12:30:56 2012 -0400 Fix statement lemma Lemma Tag 00IT didn't have enough assumptions. Fortunately, it only gets used once, in which case all necessary assumptions hold. algebra.tex | 17 ++++++++--------- 1 files changed, 8 insertions(+), 9 deletions(-) commit eefec15299710002f3cb3d4758037bd0cbee2480 Author: Aise Johan de Jong Date: Sun May 6 15:11:35 2012 -0400 The predeformation category at a point of a category fibred in groupoids artin.tex | 133 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 files changed, 133 insertions(+), 0 deletions(-) commit d551bd44af1f6b95acca7a6327975c8ffd0ac21c Author: Aise Johan de Jong Date: Sun May 6 13:47:35 2012 -0400 Small changes website Thanks Cathy scripts/make_locate.py | 4 ++-- stacks-git.html | 13 +++++++++---- 2 files changed, 11 insertions(+), 6 deletions(-) commit 3d370c0f49db5183d8144084d72c7a8851ca0b17 Author: Aise Johan de Jong Date: Sat May 5 17:37:05 2012 -0400 Check formatting strings in locate.php tags/locate.php | 16 +++++++++------- 1 files changed, 9 insertions(+), 7 deletions(-) commit 8d4b6b705689a452f901e9f5285fe78889dd49c4 Author: Aise Johan de Jong Date: Sat May 5 16:52:03 2012 -0400 Clean up locate.php The script make_locate.py now creates a subdirectory tags/tmp/code and therein files named 0000, 0001, etc (one for each tag which currently exists in the stacks projec) containing the specific information regarding the corresponding tag. The new Makefile target "code" runs the script (after building prerequisites if necessary). The tags_install target copies the tags/tmp/code directory over to the install directory. The new locate.php script when called as locate.php?tag=ABCD checks for the existence of the file code/ABCD (inside the install directory) and if it exists includes it. With this setup locate.php loads _much_ faster. Makefile | 18 ++++-- scripts/make_locate.py | 151 +++++++++++++++--------------------------------- tags/locate.php | 31 ++++++++++ 3 files changed, 91 insertions(+), 109 deletions(-) commit fde37c164e75efc9129c28cef8517db8f63012b1 Author: Aise Johan de Jong Date: Sat May 5 14:29:14 2012 -0400 Fix references formal-defos.tex | 2 +- scripts/fix_titles_refs.py | 1 + tags/tags | 4 ++-- 3 files changed, 4 insertions(+), 3 deletions(-) commit 136a9d88ad4f47176c20c3a28c6d46b64be267d5 Author: Aise Johan de Jong Date: Sat May 5 13:36:22 2012 -0400 Skeletion chapter on Artin's Axioms Makefile | 2 +- artin.tex | 83 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ browse.html | 36 ++++++++++++++--------- chapters.tex | 1 + formal-defos.tex | 41 +-------------------------- preamble.tex | 1 + tags/Makefile | 2 +- 7 files changed, 110 insertions(+), 56 deletions(-) commit 6bb230916504b9fad68a91f290a85db2000fb266 Author: Aise Johan de Jong Date: Sat May 5 10:43:26 2012 -0400 Improve Nakayama's lemma Long overdue. algebra.tex | 90 +++++++++++++++++++++++++++++++++++++++++++--------------- 1 files changed, 66 insertions(+), 24 deletions(-) commit e282cccc95f72f834a72e7737c7a8c44b155d380 Author: Aise Johan de Jong -- Strider Date: Fri May 4 09:05:22 2012 -0400 TAGS: Added new tags tags/tags | 32 ++++++++++++++++++++++++++++++++ 1 files changed, 32 insertions(+), 0 deletions(-) commit 382257e8b471d87cd88af0778951c765682c0bef Author: Aise Johan de Jong Date: Fri May 4 09:03:33 2012 -0400 Add links to references on tag lookup page scripts/make_locate.py | 41 ++++++++++++++++++++++++++++++++--------- 1 files changed, 32 insertions(+), 9 deletions(-) commit bb7755fdf5d0d9da7a0df654a2b44d3f5136b42a Author: Aise Johan de Jong Date: Fri May 4 06:58:15 2012 -0400 Adding more to tag lookup page This adds the text of items, sections, subsections, subsubsections, equations and proofs to be printed on the lookup page. scripts/functions.py | 4 +- scripts/make_locate.py | 216 ++++++++++++++++++++++++++++++++++++++++++++---- 2 files changed, 203 insertions(+), 17 deletions(-) commit dd870a6a8380569bc7642d52b84c943f28d3fc0c Author: Aise Johan de Jong Date: Thu May 3 19:03:12 2012 -0400 Fix formatting of some references smoothing.tex | 2 +- spaces-properties.tex | 6 +++--- 2 files changed, 4 insertions(+), 4 deletions(-) commit 9c51daacb470ad49b75dff9e7daaf83661d559f1 Author: Aise Johan de Jong Date: Thu May 3 18:57:04 2012 -0400 Fix references and tags spaces-properties.tex | 6 +++--- tags/tags | 14 +++++++------- 2 files changed, 10 insertions(+), 10 deletions(-) commit 3b3c53693a5c163bcfa583372c198e036d24d792 Author: Aise Johan de Jong Date: Thu May 3 16:03:36 2012 -0400 Normalize use of item labels Also check for this in parse.py algebra.tex | 214 +++++++++++++++++++++++++++++--------------------- more-morphisms.tex | 19 +++-- schemes.tex | 5 +- scripts/functions.py | 9 ++ scripts/parse.py | 31 +++++++- sets.tex | 20 +++-- sites.tex | 16 +++-- topology.tex | 37 ++++++--- 8 files changed, 221 insertions(+), 130 deletions(-) commit d8bbcd1bca9f03a3b536671229840b299162d051 Author: Aise Johan de Jong Date: Tue May 1 20:07:31 2012 -0400 Artin's approximation theorem For local G-rings. Follows from Popescu's theorem in our setup. smoothing.tex | 155 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 files changed, 155 insertions(+), 0 deletions(-) commit fe245dbf794663ec36ae509088573b44af786d9c Author: Aise Johan de Jong Date: Tue May 1 18:53:10 2012 -0400 Strict henselizations of G-rings are G-rings These sorts of lemmas never "look good". Maybe that's why I don't like henselian local rings? Still this result is natural and potentially useful. more-algebra.tex | 64 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 files changed, 64 insertions(+), 0 deletions(-) commit 6a6cf57a898ca07ed9f0a912e3111fa2b7289ae4 Author: Aise Johan de Jong Date: Tue May 1 18:52:07 2012 -0400 Permanence of properties under henselization Moved from etale-cohomology.tex to more-algebra.tex Also expanded and clarified a bit. descent.tex | 18 +-- etale-cohomology.tex | 214 +---------------------------- etale.tex | 9 +- more-algebra.tex | 373 ++++++++++++++++++++++++++++++++++++++++++++++++++ 4 files changed, 384 insertions(+), 230 deletions(-) commit 19fcc8ac549b40698bf4d631ded00d89794d99c9 Author: Aise Johan de Jong Date: Tue May 1 18:48:42 2012 -0400 Geometrically regular over separable algebraic Besides some small changes this commit contains the following result: If k ---> k' ---> A are ring maps with k'/k an algebraic separable extension, then A is geometrically regular over k if and only if A is geometrically regular over k'. This takes a bit of work to prove as you have to "think about it right". algebra.tex | 135 +++++++++++++++++++++++++++++++++++++++++++++++----------- 1 files changed, 109 insertions(+), 26 deletions(-) commit 39889292c0437bfa3000e8a73b804e0b80ee6eeb Author: Aise Johan de Jong Date: Mon Apr 30 20:22:40 2012 -0400 Small changes algebra.tex | 2 +- formal-defos.tex | 12 +++++------- 2 files changed, 6 insertions(+), 8 deletions(-) commit 65375f0ec080165b53987c4f5d30a0dff4d85bf7 Author: Aise Johan de Jong Date: Sun Apr 29 16:51:48 2012 -0400 Skeleton section regular morphisms of schemes more-morphisms.tex | 146 +++++++++++++++++++++++++++++++++++++++++++++++++++- varieties.tex | 16 ++++-- 2 files changed, 155 insertions(+), 7 deletions(-) commit e5799d072b2fdfd85a9e39ccd87ed09d950ce805 Author: Aise Johan de Jong Date: Sun Apr 29 15:48:45 2012 -0400 Move a lemma + fallout algebra.tex | 45 +++++++++++++++++++++++++++++++++++++++------ more-algebra.tex | 46 +++++++++------------------------------------- properties.tex | 2 +- tags/tags | 2 +- 4 files changed, 50 insertions(+), 45 deletions(-) commit eb2e34e39b350a25b7671d327e0327d4af2daade Author: Aise Johan de Jong Date: Sun Apr 29 13:24:19 2012 -0400 Closedness singular locus Translation into schemes language algebra.tex | 7 ++-- morphisms.tex | 84 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ properties.tex | 35 +++++++++++++++++++++++ 3 files changed, 122 insertions(+), 4 deletions(-) commit 5b2c72403509c113c7c259d2747accec754acf0f Author: Aise Johan de Jong Date: Sun Apr 29 12:44:21 2012 -0400 Explicitly reference "Serre's conditions" coherent.tex | 42 +++++++------------------------------- descent.tex | 2 +- modules.tex | 3 +- properties.tex | 60 ++++++++++++++++++++++++++++++++++++++++++++++++------- tags/tags | 6 ++-- 5 files changed, 66 insertions(+), 47 deletions(-) commit 71b18359a92539168f1c91cc87394c44f87e3cc9 Author: Aise Johan de Jong Date: Fri Apr 27 16:00:22 2012 -0400 Skeleton section about excellent rings more-algebra.tex | 118 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 files changed, 118 insertions(+), 0 deletions(-) commit 0cd691bbfb7c7b02efb0055232bbc2bd39a12d44 Author: Aise Johan de Jong Date: Fri Apr 27 10:09:12 2012 -0400 Tags: Added new tags tags/tags | 77 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 files changed, 77 insertions(+), 0 deletions(-) commit 9f994d9f12cae86a08ee58fdbf181a65843bea5e Author: Aise Johan de Jong Date: Fri Apr 27 09:48:21 2012 -0400 Ubiquity of G-rings more-algebra.tex | 22 ++++++++++++++++++++++ 1 files changed, 22 insertions(+), 0 deletions(-) commit ae5ea252b3fc6e69a2e0b90a73242ba2944bfb08 Merge: f8de66b c0832cc Author: Aise Johan de Jong Date: Fri Apr 27 09:33:42 2012 -0400 Merge branch 'fs' commit c0832cc960f990b6fc3a191fc3a4c18028acf9cc Author: Aise Johan de Jong Date: Fri Apr 27 09:25:29 2012 -0400 Remove organizational remarks Actually, the eventual path taken was a bit different. smoothing.tex | 68 --------------------------------------------------------- 1 files changed, 0 insertions(+), 68 deletions(-) commit 97a479c50343a67872f75890ffa0b033b1954417 Author: Aise Johan de Jong Date: Fri Apr 27 09:24:20 2012 -0400 Finite type over G-ring is G-ring The proof is now finished. more-algebra.tex | 88 ++++++++++++++++++++++++++++++++++++++++++++++-------- 1 files changed, 75 insertions(+), 13 deletions(-) commit ae2104e7b07c67a273aba88acc8c53b5a7c6a0a5 Author: Aise Johan de Jong Date: Thu Apr 26 16:14:24 2012 -0400 Small fix more-algebra.tex | 5 ++--- 1 files changed, 2 insertions(+), 3 deletions(-) commit 2fa1277ec1c1806a51ba4b4a2fdf0e92af5f4c4b Author: Aise Johan de Jong Date: Thu Apr 26 10:38:21 2012 -0400 Formally smooth in the m-adic topology implies regular Again using the trick with derivations. This time using in an essential way that derivations can be lifted to formally smooth over rings... Cool. algebra.tex | 17 ++++--- more-algebra.tex | 149 ++++++++++++++++++++++++++++++++++++++++++++++++++--- 2 files changed, 150 insertions(+), 16 deletions(-) commit 0f27d18184c3c5d88e74f9c3ba00717d12bb0d5a Author: Aise Johan de Jong Date: Wed Apr 25 17:26:48 2012 -0400 Deforming fs algebras more-algebra.tex | 97 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 files changed, 97 insertions(+), 0 deletions(-)