文档介绍：Twenty-four hours of local cohomology
Srikanth Iyengar
Graham J. Leuschke
Anton Leykin
Claudia Miller
Ezra Miller
Anurag K. Singh
Uli Walther
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Department of Mathematics, University of Nebraska, 203 Av-
ery Hall, Lincoln, NE 68588
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Mathematics Department, Syracuse University, 215 Carnegie
Hall, Syracuse, NY 13244
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Institute for Mathematics and its Applications, 207 Church
Street ., Minneapolis, MN 55455
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Mathematics Department, Syracuse University, 215 Carnegie
Hall, Syracuse, NY 13244
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School of Mathematics, University of Minnesota, 127 Vin-
cent Hall, 206 Church Street ., Minneapolis, MN 55455
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Department of Mathematics, University of Utah, 155 S 1400
E, Salt Lake City, UT 84112
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Department of Mathematics, Purdue University, 150 North
University Street, West Lafayette, IN 47907
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To our teachers
Contents
Preface xi
Introduction xiii
Lecture 1. Basic notions 1
1. Algebraic sets 1
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2. Krull dimension of a ring 3
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3. Dimension of an algebraic set 6
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4. An extended example 9
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5. Tangent spaces and regular rings 10
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6. Dimension of a module 12
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Lecture 2. Cohomology 15
1. Sheaves 16
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2. Cechˇ cohomology 18
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3. Calculus versus topology 23
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4. Cechˇ cohomology and derived functors 27
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Lecture 3. Resolutions and derived functors 29
1. Free, projective, and flat modules 29
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2. Complexes 32
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3. Resolutions 34
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4. Derived functors 36
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Lecture 4. Limits 41
1. An example from topology 41
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2. Direct limits 42
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3. The category of diagrams 44
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4. Exactness 45
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5. Diagrams over diagrams 48
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6. Filtered posets 49
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7. Diagrams over the pushout poset 51
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8. I