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An on-line math course

已有 7088 次阅读 2013-11-28 04:00 |系统分类:科研笔记

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.   Introductiononline
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2.   Conventionsonline
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3.   Set Theoryonline
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4.   Categoriesonline
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5.   Topologyonline
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6.   Sheaves on Spacesonline
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7.   Sites and Sheavesonline
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8.   Stacksonline
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9.   Commutative Algebraonline
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10.   Brauer groupsonline
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11.   Homological Algebraonline
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12.   Derived Categoriesonline
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13.   Simplicial Methodsonline
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14.   More on Algebraonline
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15.   Smoothing Ring Mapsonline
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16.   Sheaves of Modulesonline
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17.   Modules on Sitesonline
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18.   Injectivesonline
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19.   Cohomology of Sheavesonline
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20.   Cohomology on Sitesonline
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21.   Hypercoveringsonline
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Schemes




22.   Schemesonline
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23.   Constructions of Schemesonline
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24.   Properties of Schemesonline
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25.   Morphisms of Schemesonline
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26.   Cohomology of Schemesonline
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27.   Divisorsonline
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28.   Limits of Schemesonline
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29.   Varietiesonline
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30.   Topologies on Schemesonline
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31.   Descentonline
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32.   Derived Categories of Schemesonline
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33.   More on Morphismsonline
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34.   More on Flatnessonline
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35.   Groupoid Schemesonline
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36.   More on Groupoid Schemesonline
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37.   Étale Morphisms of Schemesonline
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Topics in Scheme Theory




38.   Chow Homology and Chern Classesonline
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39.   Adequate Modulesonline
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40.   Dualizing Complexesonline
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41.   Étale Cohomologyonline
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42.   Crystalline Cohomologyonline
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43.   Pro-étale Cohomologyonline
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Algebraic Spaces




44.   Algebraic Spacesonline
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45.   Properties of Algebraic Spacesonline
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46.   Morphisms of Algebraic Spacesonline
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47.   Decent Algebraic Spacesonline
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48.   Cohomology of Algebraic Spacesonline
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49.   Limits of Algebraic Spacesonline
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50.   Divisors on Algebraic Spacesonline
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51.   Topologies on Algebraic Spacesonline
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52.   Descent and Algebraic Spacesonline
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53.   Derived Categories of Spacesonline
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54.   More on Morphisms of Spacesonline
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55.   Algebraic Spaces over Fieldsonline
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56.   Groupoids in Algebraic Spacesonline
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57.   More on Groupoids in Spacesonline
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58.   Bootstraponline
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59.   Quotients of Groupoidsonline
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Deformation Theory




60.   Formal Deformation Theoryonline
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61.   Deformation Theoryonline
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62.   The Cotangent Complexonline
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Algebraic Stacks




63.   Algebraic Stacksonline
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64.   Examples of Stacksonline
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65.   Sheaves on Algebraic Stacksonline
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66.   Criteria for Representabilityonline
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67.   Artin's axiomsonline
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68.   Quot and Hilbert Spacesonline
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69.   Properties of Algebraic Stacksonline
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70.   Morphisms of Algebraic Stacksonline
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71.   Cohomology of Algebraic Stacksonline
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72.   Derived Categories of Stacksonline
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73.   Introducing Algebraic Stacksonline
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Miscellany




74.   Examplesonline
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75.   Exercisesonline
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76.   A Guide to the Literatureonline
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77.   Desirablesonline
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78.   Coding Styleonline
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79.   Obsoleteonline
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80.   GNU Free Documentation Licenseonline
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81.   Auto generated index

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