Talked to Deglise Proper descent (stronger than etale?) can be used for example in de Rham cohomology I think, CD uses thm of Cioc??? to prove Nisnevich descent for rigid cohomology. Also: Machinery of CD might possibly give independence of l, because they can compare l-adic and rigid in DM of a valuation ring, after tensoring with something big maybe, since the machine works also for nonregular things I think.
mumford: the red book of varieties and schemes
modern analysis links: www.mth.kcl.ac.uk/MAO
All notes in the black thing on my desk
everything under research and maths docs on gmail
IHES preprints: http://www.ihes.fr/jsp/site/Portal.jsp?page_id=65 Have sweeped from Jan 2006 up to May 2009
http://www.math.univ-paris13.fr/~hebert/GT_CE_fr.html
http://www.math.uni-muenster.de/u/peter.schneider/Archiv_index.html
Stuff originally intended for my webpage, and coming from my webpage:
http://www.artofproblemsolving.com/Resources/Papers/SatoNT.pdf Check also other resources here.
find also teh actual imo texts
http://uk.youtube.com/user/TheCatsters
William Wu\'s wonderful website of neat problems (and neat math).
http://mathcircle.berkeley.edu/cnt.pdf check other resources here as well http://www.math.uu.nl/people/beukers/getaltheorie/pen0795.pdf
http://www.cs.otago.ac.nz/staffpriv/malbert/IMO/Team2003/Training/004_NS.pdf
www.bhargav.com/books/list2.html
www.stat.ufl.edu/~ssaha/textbooksinMath.htm
Finite simple gruops: http://www.maths.qmul.ac.uk/~raw/fsgs.html
Lurie: Elliptic cohom, Toen on http://front.math.ucdavis.edu/0312.5262, McLarty on simplicity (on circle), Frenkel, Toen on http://front.math.ucdavis.edu/math.AG/0604504, Morel Trieste lectures, Severitt, Dwyer-Spalinski
Topological modular forms reading
http://thales.math.uqam.ca/~anelm/hag.html
http://www.jde27.co.uk/
http://www.fields.utoronto.ca/programs/scientific/06-07/homotopy/courses/index.html
http://www.rzuser.uni-heidelberg.de/~hb3/notes.html
http://arxiv.org/pdf/0707.3216.pdf (Moravas survey, for the front page)
http://www.w3schools.com/
split research into local Langlands page and motivic stable homotopy page
www.Vlib-math.de
http://cornellmath.wordpress.com/
download from gigapedia, search for hodge, motivic, motives, etc
download from K-theory archive
Gene Lewis article for group cohomology
Navarro-Aznar, Guillen, Zariski,
Next Einstein at Facebook: http://www.facebook.com/group.php?gid=12307234797&ref=mf
Links at http://www.institut.math.jussieu.fr/liens/liens.html, and maybe other Paris pages
Hyperbolic geometry: Ref to SUMS book
Systematic Wikipedia sweep?
Systematic readthrough of MR classification. Link to interesting codes from relevant places in the database.
Links from http://www.math.purdue.edu/~jinhyun/
Download from http://www.mathematik.uni-regensburg.de/preprints/Forschergruppe/ListeA-Z.htm
Download from pages under Google search: Huber-Klawitter
http://www.aps-pub.com/proceedings/1451/Weil.pdf about the life of Weil (short)
All browser bookmarks (have finished job computer), and various blogs (under Blogs). Link to blogs from front page.
Add Geom Langlands entry, with link: http://www.ma.utexas.edu/users/benzvi/Langlands.html
http://www.tac.mta.ca/tac/volumes/14/19/14-19.pdf
http://north.ecc.edu/alsani/descent.html
http://www.intute.ac.uk/sciences/mathematics/
Download all example sheets and course material from DPMMS site.
Incorporate emails? In particular, answers from Scholl.
Explore the MathSciNet classification system
http://www.numbertheory.org/ for webpages and links to mathematicians
http://arxiv.org/abs/0707.0904
http://math.ucr.edu/home/baez/qg-spring2007/
http://www.ams.org/bookstore?fn=20&arg1=pspumseries&item=PSPUM-67
http://www.numdam.org/numdam-bin/fitem?id=CTGDC_1987__28_2_89_0
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6W9F-4H3JJHP-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=dd710a44508a6b839ba12f8ae6adb4f2
http://www.fields.utoronto.ca/programs/scientific/06-07/homotopy/seminar.html
http://en.wikipedia.org/wiki/Nerve_(category_theory)
Check handbook of algebra, for example for higher algebraic K-theory
http://www.math.uiuc.edu/~dan/Lectures/2007-07-Hangzhou/
http://math.berkeley.edu/~teichner/Courses/DAGdetails.pdf
http://www.iop.org/EJ/abstract/0036-0279/49/2/L10
http://www.math.columbia.edu/~dejong/algebraic_geometry/desirables.pdf
http://www.math.mcgill.ca/goren/SeminarOnCohomology/
To find good recent material I am not aware of, try to look at papers referring to amazing classics in MathSciNet. For example to Thomason, Grothendieck, Beilinson etc.
Use the fact that good (foundational) references often come up under MR reviews of not so foundational articles.
Should also go through and incorporate links to my paper notes.
All notes from discussions with Scholl
Add refs to everything in the 1979 volumes.
Go through the PROGRAM of thr Motives volumes
Could search certain classification codes, for example 14C25 (algebraic cycles) on Zentralblatt or MathSciNet
R. Hartshorne, Residues and duality, Lecture Notes in Math. 20, Springer-Verlag, 1966. (add somewhere)
Enriched category: Kelly introduction. Also perhaps: Bird, Kelly, Power, Street - Flexible limits in 2-categories. Blackwell, Kelly, Power - Two-dimensional monad theory.
Cotangent complex: Ref to Illusie (?) and to Goerss-Schemmerhorn pp. 32. Def given there: The cotangent complex for a commutative -algebra is the simplicial -module given by the \"total left derived functor of differentials\". Its homotopy groups seem to be the André-Quillen homology of .
Algebraic space: Ref to Artin: Construction techniques for algebraic spaces. Artin writes that Algebraic stacks are more general than algebraic spaces, which are more general than schemes. Roughly, an algebraic space is a quotient of a sum of affine schemes by an equivalence relation which is étale over this sum. Ref: Knutson. Have a basic existence thm: One considers a contravariant functor from -schemes to sets. Such a functor is represented by an algebraic space locally of finite type over iff a list of five conditions is satisfied, including: (i) is an étale sheaf, (ii) is locally of finite presentation, (iv) is effectively pro-representable. These conditions \"follow a general pattern established by Grothendieck\", ref to Murre: On contravariant functors… (Pub. Math. I.H.E.S., No. 23 (1964)) and Murre: Representation of unramified functors (Bourbaki). Application to representability of Hilbert and Picard functors.
Add a link to http://www.ma.utexas.edu/users/benzvi/Langlands.html and to stuff therein, for example stacks and other things.
Abelian group object: See Goerss-Schemmerhorn p. 30 for a nice discussion. Includes abelianization in model categories, and the Quillen homology of an object as the total left derived functor of abelianization.
Higher cats:
References: - Leinster - Higher Operads, Higher Categories - http:// www.maths.gla.ac.uk/~tl/book.html - Cheng/Willerton \"The Catsters\" - various videos on YouTube (if you haven\'t come across these before, they\'re great fun, though fairly basic), particularly the \"Spans\" and \"Monads\" series. - Cheng/Lauda - The Guideook - http://www.dpmms.cam.ac.uk/~elgc2/ guidebook/ - Leinster - the \"10 definitions paper\" - http://arxiv.org/abs/math/ 0107188
Noncommutative geometry Algebraic geometry Algebraic topology Category theory
When can we speak of a \"category A object in category B\". E.g. group object in the category of schemes. Why not topological space object in the category of groups?
Do a questions section, for scholl, hyland etc
mathscinet all interesting authors, including fields med!!
When/how does structure on representing objects force the corresponding representable functor to land in a more structured category that Set? Perhaps Rognes has an idea?
Is HZ initial in ring spectra?
Add more details on representability for motivic cohomology, and trivial circle for étale
have skimmed arxiv:
KT (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory): May 06 - Mar 07 NT: Jan 07 - Mar 07 Algebraic Topology: Oct 06 - Mar 07
K-theory preprints: 3 Jul 06 - 17 Apr 07
Ktheory handbook
Basic reading: Kashiwara, Adams x2, Friedlander, Liu, FGA. Bott & Tu, Jardine notes x2.
For p-adic CTs in Algebraic Geometry, check the reference [P] in this article by Illusie
For each of the really interesting authors, listed in this Glossary, go through all publications (Voevodsky, Toen, …) including K-theory archive, arXiv, MathSciNet, and their web page. Also Deninger. See Mathematicians
Go through list of Springer LNM.
After this, work through the general picture of motivic homotopy theory, and try to compute or prove something. Also, work through the database and fill out details for Algebraic Geometry and CAT worlds.
Could also go through: Bourbaki, jornals such as TAC, K-theory and homology, …
Possibly all LNM and all Bourbaki reports.
http://www.ams.org/notices/200710/tx071001323p.pdf
Index of Weibel
Neukirch (both)
Spectral sequences, Hodge theory?
Ga igenom dokument pa min dator
Relevant stuff from Wikipedia.
Arxiv: Algebraic Topology, Algebraic Geometry, KT (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory) (K-theory)
http://www.math.uio.no/~rognes/cas/application.html
For MathSciNet, it probably takes to much time to go through everything returned by \"cohomology\", \"K-theory\" etc. Try to be more clever. Perhaps one could search for \"stable\", \"stable homotopy\", \"spectral sequence\", \"spectra\".
TAC: http://www.tac.mta.ca/tac/index.html#vol12
http://www.mathematik.uni-bielefeld.de/documenta/
K-theory archive (have checked up to K0860, i.e. July 2007)
Web resources in maths
http://eom.springer.de/default.htm
Wikipedia.
http://www.justpasha.org/math/links/books/online.html
Brian Conrad’s web page, especially his books. Have tried to save some, problems with tar extraction
have downloaded book on homotopy theory, but need more fonts. see link from pashas page above
Check monstruous moonshine at Wiki. Also check IM
http://us.geocities.com/alex_stef/mylist.html
jmilne
http://mthwww.uwc.edu/wwwmahes/files/math01.htm#ref01
Web links to Rosen’s book on Elementary NTh: http://www.aw-bc.com/rosen/weblinks.html
See also Vakil’s link to Kedlaya, for competitions
For competition material: Geoff Smith has some manuals used for UK team, and other nice stuff perhaps
nLab page on Indexing to do