博文
An on-line math course
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This is a very impressive open resource for mathematics. It is a pity that there is nothing like that in physics.
from http://stacks.math.columbia.edu/browse
| 1. Introduction | online | tex | pdf | |
| 2. Conventions | online | tex | pdf | |
| 3. Set Theory | online | tex | pdf | |
| 4. Categories | online | tex | pdf | |
| 5. Topology | online | tex | pdf | |
| 6. Sheaves on Spaces | online | tex | pdf | |
| 7. Sites and Sheaves | online | tex | pdf | |
| 8. Stacks | online | tex | pdf | |
| 9. Commutative Algebra | online | tex | pdf | |
| 10. Brauer groups | online | tex | pdf | |
| 11. Homological Algebra | online | tex | pdf | |
| 12. Derived Categories | online | tex | pdf | |
| 13. Simplicial Methods | online | tex | pdf | |
| 14. More on Algebra | online | tex | pdf | |
| 15. Smoothing Ring Maps | online | tex | pdf | |
| 16. Sheaves of Modules | online | tex | pdf | |
| 17. Modules on Sites | online | tex | pdf | |
| 18. Injectives | online | tex | pdf | |
| 19. Cohomology of Sheaves | online | tex | pdf | |
| 20. Cohomology on Sites | online | tex | pdf | |
| 21. Hypercoverings | online | tex | pdf | |
| Schemes | ||||
| 22. Schemes | online | tex | pdf | |
| 23. Constructions of Schemes | online | tex | pdf | |
| 24. Properties of Schemes | online | tex | pdf | |
| 25. Morphisms of Schemes | online | tex | pdf | |
| 26. Cohomology of Schemes | online | tex | pdf | |
| 27. Divisors | online | tex | pdf | |
| 28. Limits of Schemes | online | tex | pdf | |
| 29. Varieties | online | tex | pdf | |
| 30. Topologies on Schemes | online | tex | pdf | |
| 31. Descent | online | tex | pdf | |
| 32. Derived Categories of Schemes | online | tex | pdf | |
| 33. More on Morphisms | online | tex | pdf | |
| 34. More on Flatness | online | tex | pdf | |
| 35. Groupoid Schemes | online | tex | pdf | |
| 36. More on Groupoid Schemes | online | tex | pdf | |
| 37. Étale Morphisms of Schemes | online | tex | pdf | |
| Topics in Scheme Theory | ||||
| 38. Chow Homology and Chern Classes | online | tex | pdf | |
| 39. Adequate Modules | online | tex | pdf | |
| 40. Dualizing Complexes | online | tex | pdf | |
| 41. Étale Cohomology | online | tex | pdf | |
| 42. Crystalline Cohomology | online | tex | pdf | |
| 43. Pro-étale Cohomology | online | tex | pdf | |
| Algebraic Spaces | ||||
| 44. Algebraic Spaces | online | tex | pdf | |
| 45. Properties of Algebraic Spaces | online | tex | pdf | |
| 46. Morphisms of Algebraic Spaces | online | tex | pdf | |
| 47. Decent Algebraic Spaces | online | tex | pdf | |
| 48. Cohomology of Algebraic Spaces | online | tex | pdf | |
| 49. Limits of Algebraic Spaces | online | tex | pdf | |
| 50. Divisors on Algebraic Spaces | online | tex | pdf | |
| 51. Topologies on Algebraic Spaces | online | tex | pdf | |
| 52. Descent and Algebraic Spaces | online | tex | pdf | |
| 53. Derived Categories of Spaces | online | tex | pdf | |
| 54. More on Morphisms of Spaces | online | tex | pdf | |
| 55. Algebraic Spaces over Fields | online | tex | pdf | |
| 56. Groupoids in Algebraic Spaces | online | tex | pdf | |
| 57. More on Groupoids in Spaces | online | tex | pdf | |
| 58. Bootstrap | online | tex | pdf | |
| 59. Quotients of Groupoids | online | tex | pdf | |
| Deformation Theory | ||||
| 60. Formal Deformation Theory | online | tex | pdf | |
| 61. Deformation Theory | online | tex | pdf | |
| 62. The Cotangent Complex | online | tex | pdf | |
| Algebraic Stacks | ||||
| 63. Algebraic Stacks | online | tex | pdf | |
| 64. Examples of Stacks | online | tex | pdf | |
| 65. Sheaves on Algebraic Stacks | online | tex | pdf | |
| 66. Criteria for Representability | online | tex | pdf | |
| 67. Artin's axioms | online | tex | pdf | |
| 68. Quot and Hilbert Spaces | online | tex | pdf | |
| 69. Properties of Algebraic Stacks | online | tex | pdf | |
| 70. Morphisms of Algebraic Stacks | online | tex | pdf | |
| 71. Cohomology of Algebraic Stacks | online | tex | pdf | |
| 72. Derived Categories of Stacks | online | tex | pdf | |
| 73. Introducing Algebraic Stacks | online | tex | pdf | |
| Miscellany | ||||
| 74. Examples | online | tex | pdf | |
| 75. Exercises | online | tex | pdf | |
| 76. A Guide to the Literature | online | tex | pdf | |
| 77. Desirables | online | tex | pdf | |
| 78. Coding Style | online | tex | pdf | |
| 79. Obsolete | online | tex | pdf | |
| 80. GNU Free Documentation License | online | tex | pdf | |
| 81. Auto generated index |
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