Some mathematical resources

Online Bibliothek
  1. Arxiv
  2. Purdue University Library
  3. University of Chicago Library
  4. AMS Mathscinet
  5. SGA
  6. Numerisation de documents anciens mathematiques
  7. JSTOR
  8. Goettingen Library
  9. ICTP Open Access Archive
  10. Mathematica Scandinavica
  11. Korea National Digital Science Library
  12. Canadian Journal of Mathematics : since 1997
  13. Journal of Algebraic Geometry : since 2002
  14. Mathematics of USSR-Sbornik
  15. Biblioteka Wirtualna Matematyki : Fundamenta Mathematicae (1920-1993) Studia Mathematica (1929-1964) Prace matematyczno-fizyczne (1888-1952)
  16. Revista de Matematicas Aplicadas (1994-2002)
  17. Dieper, DIgitised European PERiodicals : Monatshefte fur Mathematik und Physik (1890-1918)
  18. EMIS, European Mathematical Information Service Jahrbuch uber die Fortschritte der Mathematik (1868-1931)

Some notes for my past talks
  1. My topic Proposal: The Riemann-Roch Theorem, Intersection Theory and Minimal Models for Surfaces I gave two talks based on it early in 2003.
  2. Proofs of theorems for the topic proposal: Some proofs might be false. I am too lazy to fix them. But, I am pretty sure that it can be helpful if you just began to study algebraic surfaces.
  3. Introduction to higher algebraic K-theory, Talk on Dec. 3, 2003
  4. Hilbert's 3rd problem: My Pizza seminar talk. Pictures are missing. This is also related to my thesis work. Talk given in Mar. 2004
  5. A survey on Gersten resolution and Bloch's formula : I gave a talk on it in Apr. 2004
  6. Additive Higher Chow Groups I, II My talk at KIAS in Aug. 2004 and in Feb. 2005 at Chicago.
  7. Classical regulator on Riemann surfaces: It reviews a construction of regulators on K_2 (X) for a Riemann surfaces X. Talk in Jan. 2005
  8. Algebraic cycles and Euclidean Geometry: My talk at Brown University on Mar. 22, 2005. It is very relevant to my thesis work.
  9. Regulators in algebraic geometry: My talk at KIAS in Jul. 2005. It is a general survey on regulators from various points of view: Beilinson's conjectures on special values of L-functions, Chern characters, cycles class maps, Abel-Jacobi maps, etc. I do not have a note for my second talk. For this, please read my preprints.
  10. Residues on an arbitrary variety: This is a note for my talk at Sogang University in Aug. 2005. This is about the amazing residue theory of Parshin-Lomadze.

Some links
  1. The Grothendieck Circle
  2. Professor Bloch's recent papers
  3. Chris's math links
  4. Research group Esnault-Viehweg at Uni Essen

Some lecture notes/papers written by others
  1. Stacks pdf file by Aaron Bertram at Utah.
  2. Green's conjecture for canonical curves by Claire Voisin.
  3. Construction of the Hilbert Schemes by Aaron Bertram at Utah.
  4. Genus Zero Gromov-Witten Invariants by Aaron Bertram at Utah.
  5. Chris' topic proposal: Faltings' Theorem
  6. Spring 2003 course note: Algebraic Cycles by Professor Bloch : This course is currently going on, so, it is going to be updated whenever there is a class. Because I do not necessarily understand everything from the class, my note can possibly be not complete. I try my best, but sometimes it is not avoidable.
  7. An Introduction to Algebraic K-theory: by Charles Weibel. Unfinished work, but, it is still very useful.
  8. Grothendieck topologies and descent by A. Vistoli at ICTP summer school on FGA, July 2003, Trieste, Italy
  9. Construction of Hilbert and Quot schemes by N. Nitsure at ICTP summer school on FGA, July 2003, Trieste, Italy
  10. Grothendieck's existence theorem in formal geometry by L. Illusie at ICTP summer school on FGA, July 2003, Trieste, Italy
  11. Picard schemes by S.L. Kleiman at ICTP summer school on FGA, July 2003, Trieste, Italy TO APPEAR. I have my note from the classes, but, Prof. Kleiman said that he will finish making the note as soon as possible, so, please be patient.
  12. Local properties of Hilbert schemes and Hilbert schemesof points by L. Göttsche at ICTP summer school on FGA, July 2003, Trieste, Italy
  13. Michigan's Dolgachev's lecture notes
  14. Daniel Grayson's Higher Algbraic K-theory lecture note, Spring, 2003
  15. Professor Madhav Nori's class note: K-theory, Spring 2004: Current version 0.20040927001. It requires a revision so that please do not print it out yet. I typed up all of them.
  16. Professor Madhav Nori's class note: K-theory and related topics, Autumn 2004: unfinished yet. I am working on it.
  17. Professor Victor Ginzburg's class note: Quivers, Winter 2005: I did not attend all classes so that some notes are missing.
  18. Professor Victor Ginzburg's class note: Semisimple groups, Winter 2005: I did not attend all classes so that some notes are missing.
  19. Professor Vadim Vologodsky's class note: p-adic Hodge theory, Winter 2005
  20. Professor Alexander Merkurjev from UCLA's Abert lectures at Chicago, April 2005
  21. Professor Spencer Bloch's class notes on Periods, Spring 2005: Part 1 is from Mar. 29, 2005 to Apr. 21, 2005; Part 2 is the rest.

Some personal notes I typed for myself
  1. Personal notes on K-functors and the Grothendieck-Riemann-Roch theorem: It is basically a summary of Yuri Manin's 'Lectures on K-functors in Algebraic Geometry'.
  2. Personal notes on Higher Algebraic K-theory: link broken
  3. Delign-Beilinson Cohomology : Personal note
  4. A personal note on Grothendieck spectral sequence: Subject to update without notice.
  5. A personal note on normal schemes: Subject to update without notice.
  6. A personal note on normalization: Subject to update without notice.
  7. A personal note on \'etale Poincar\'e duality: Subject to update without notice.
  8. A personal note on \'etale Purity theorem: Subject to update without notice.
  9. A personal note on the proper base change theorem in \'etale cohomology: Subject to update without notice.
  10. A personal note on the construction of cohomology groups with compact support in \'etale cohomology: Subject to update without notice.
  11. A personal review note on completion: Subject to change without notice.
  12. A personal note on infinite dimensional Galois theory: Subject to change without notice.
  13. A personal note on $l$-adic sheaf: Subject to change without notice.
  14. A personal note on proper-smooth base change theorem in \'etale cohomology: Subject to change without notice.
  15. A personal note on the comparison theorem of \'etale cohomology with the complex cohomology: Subject to change without notice.
  16. l-adic K\"unneth formula
  17. A personal note on the cycle class map and Chern classes in l-adic cohomology: Subject to change without notice.
  18. A personal note on the Lefschetz fixed point theorem on l-adic cohomology: Subject to change without notice.
  19. A personal note on the Weil conjectures without the Riemann hypothesis: Subject to change without notice.
  20. A personal note on the Picard schemes: Subject to change without notice.
  21. A personal note on derived categories: Subject to change without notice.
  22. A personal note on triangulated categories: Subject to change without notice.
  23. A personal note on Algebraic Cycle Complexes: Subject to change without notice.
  24. A personal note on condition for finiteness of length: Subject to change without notice.
  25. A personal note on Hochschild homology and Cyclic homology: Subject to change without notice.
  26. A brief personal note on relative algebraic K-theory: Subject to change without notice.
  27. A personal note on the additive Bloch group: Subject to change without notice.
  28. A personal note on deformation of complex manifolds: Subject to change without notice.
  29. A personal note on symbols: Subject to change without notice.
  30. A personal note on Leray-Hirsch theorem: Subject to change without notice.
  31. A personal note on currents: Subject to change without notice.
  32. A short personal note on zero-cycles on abelian varieties: Subject to change without notice.
  33. A personal note on Tannakian categories: Subject to change without notice.
  34. On the theorem of Roitman: a personal note. Unfinished yet.
  35. A personal note on universal central extensions: subject to change without notice
  36. Examples in hypercohomology: Work in progress. Subject to change without notice.
  37. A trivia fact on line bundles
  38. On Cartier Operator: a personal note
  39. Hilbert schemes and Quot schemes for lazy dummies: a simple note for dummies. Made for people who want to know about them within an hour.
  40. A personal note on Andre-Quillen homology: Subject to change without notice.
  41. A personal note on infinitesimal deformations: Subject to change
  42. Construction of Quot schemes: a personal note: Subject to change
  43. Obstructions to lifting infinitesimal deformations: A personal note.
  44. A personal note on Functors of Artin rings: Subject to change without notice.
  45. A personal note on deformation functors associated to DGLA: Subject to change without notice.
  46. A personal note on formal function theorem: Subject to change without notice.
  47. A personal note on the Period domain and Griffiths transversality: Subject to change without notice.
  48. A personal note on Noether-Lefschetz locus: Subject to change without notice.
  49. A personal note: a cute proof of Castelnuovo-Mumford regularity theorem: subject to change without notice.
  50. A personal note on the technical lemma of Green on Noether-Lefschetz locus: subject to change without notice.
  51. A personal note on the Macaulay's theorem and the Donagi symmetrize lemma: subject to change without notice.
  52. A personal note on the first prolongation bundle: definition: subject to change without notice.
  53. A personal note: M. Green's proof of the Explicit Nother-Lefschetz theorem: subject to change without notice.
  54. A personal note on p-typical de Rham-Witt complex after Illusie: subject to change without notice.
  55. A personal note on Witt vectors: subject to change without notice.
  56. A personal note on de Rhwm-Witt complex: subject to change without notice.
  57. A personal note on Newton polygon: subject to change without notice.
  58. Personal note on operads: definition and examples: subject to change without notice.
  59. A personal note on Higher order Hochschild homology: subject to change without notice.
  60. A personal note on Rigid dualizing complexes via DGAs
  61. A personal note on lambda-decompositions for Hochschild homology
  62. A personal note on some martingale processes of polynomial type in the 1-dimensional Brownian motion
  63. A personal note on Lagrangian and Hamiltonian formalism: a sketch
  64. A personal note on basics of Hopf algebras
  65. A personal note on G_a, G_m, M_2 and GL_2
  66. A personal note on basics of Lie algebras
  67. A personal note on module-algebras over bialgebras
  68. A personal note on the Yang-Baxter equation and braided bialgebra
  69. A personal note on the Braid groups and the Yang-Baxter equation
  70. A personal note on bicrossed products of groups
  71. A personal note on bicrossed products of bialgebras
  72. A personal note on Ore extensions
  73. A personal note on connections and et cetera.
  74. The lemma of nilpotent endomorphisms
  75. A personal note on some basics of differential geometry
  76. A derivation of Lorentz transformations in special relativity
  77. Short note on pseudo-coherent and perfect complexes