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Motivic integration

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162: 134: 92: 47:. Roughly speaking, motivic integration assigns to subsets of the arc space of an algebraic variety, a volume living in the 157: 77: 80: 111: 40: 119: 48: 44: 36: 20: 122: 32: 52: 24: 151: 60: 35:. Since its introduction it has proved to be quite useful in various branches of 28: 56: 103: 63:, in motivic integration the values are geometric in nature. 55:. The naming 'motivic' mirrors the fact that unlike ordinary 141:
Arc spaces, motivic integration and stringy invariants
8: 128:Seattle lecture notes on motivic integration 163:Definitions of mathematical integration 7: 14: 120:Lecture Notes (version of 2008) 1: 27:in 1995 and was developed by 59:, for which the values are 179: 86:What is motivic measure? 23:that was introduced by 93:Lecture Notes (2019) 78:AMS Bulletin Vol. 42 112:motivic integration 110:An introduction to 98:Motivic Integration 53:algebraic varieties 41:birational geometry 17:Motivic integration 158:Algebraic geometry 45:singularity theory 37:algebraic geometry 21:algebraic geometry 49:Grothendieck ring 170: 25:Maxim Kontsevich 178: 177: 173: 172: 171: 169: 168: 167: 148: 147: 123:François Loeser 104:math.AG/9911179 95:Devlin Mallory 74: 69: 39:, most notably 33:François Loeser 19:is a notion in 12: 11: 5: 176: 174: 166: 165: 160: 150: 149: 146: 145: 144: 143: 132: 131: 130: 117: 116: 115: 101: 100: 99: 90: 89: 88: 73: 72:External links 70: 68: 65: 13: 10: 9: 6: 4: 3: 2: 175: 164: 161: 159: 156: 155: 153: 142: 139: 138: 136: 135:Lecture Notes 133: 129: 126: 125: 124: 121: 118: 114: 113: 108: 107: 105: 102: 97: 96: 94: 91: 87: 84: 83: 82: 79: 76: 75: 71: 66: 64: 62: 58: 54: 50: 46: 42: 38: 34: 30: 26: 22: 18: 140: 127: 109: 85: 61:real numbers 16: 15: 57:integration 152:Categories 67:References 81:Tom Hales 29:Jan Denef 137:W.Veys 106:A.Craw 43:and 31:and 51:of 154::

Index

algebraic geometry
Maxim Kontsevich
Jan Denef
François Loeser
algebraic geometry
birational geometry
singularity theory
Grothendieck ring
algebraic varieties
integration
real numbers
AMS Bulletin Vol. 42
Tom Hales
Lecture Notes (2019)
math.AG/9911179
motivic integration
Lecture Notes (version of 2008)
François Loeser
Lecture Notes
Categories
Algebraic geometry
Definitions of mathematical integration

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