Knowledge

Regular scheme

Source đź“ť

196: 126:. Note that the cited definition that Hartshorne gives is slightly misleading. A locally Noetherian scheme is regular if all its local rings are regular, but it is not the case for schemes which are not locally Noetherian. See the cited Stacks Project page for more details. 237: 230: 266: 174: 120: 72: 223: 55: 112: 256: 169:, North-Holland Mathematics Studies, vol. 39, North-Holland, Proposition 3.2, p. 168, 77: 261: 164: 106: 32: 8: 211: 203: 40: 24: 170: 116: 82: 17: 67: 102: 160: 207: 250: 48: 44: 136: 36: 195: 54:
For an example of a regular scheme that is not smooth, see
47:
is regular, and every regular scheme of finite type over a
137:"Section 28.9 (02IR): Regular schemes—The Stacks project" 166:
Introduction to algebraic geometry and algebraic groups
248: 231: 238: 224: 101: 159: 115:, vol. 52, Springer, p. 238, 249: 190: 56:Geometrically regular ring#Examples 13: 14: 278: 73:Dimension of an algebraic variety 194: 153: 129: 95: 1: 113:Graduate Texts in Mathematics 88: 210:. You can help Knowledge by 7: 61: 10: 283: 189: 15: 78:Glossary of scheme theory 267:Algebraic geometry stubs 141:stacks.math.columbia.edu 31:is a locally Noetherian 16:Not to be confused with 206:–related article is a 257:Algebraic geometry 204:algebraic geometry 108:Algebraic Geometry 43:everywhere. Every 25:algebraic geometry 219: 218: 103:Hartshorne, Robin 83:Smooth completion 18:regular embedding 274: 240: 233: 226: 198: 191: 181: 179: 161:Demazure, Michel 157: 151: 150: 148: 147: 133: 127: 125: 99: 282: 281: 277: 276: 275: 273: 272: 271: 247: 246: 245: 244: 187: 185: 184: 177: 158: 154: 145: 143: 135: 134: 130: 123: 100: 96: 91: 64: 21: 12: 11: 5: 280: 270: 269: 264: 259: 243: 242: 235: 228: 220: 217: 216: 199: 183: 182: 175: 152: 128: 121: 93: 92: 90: 87: 86: 85: 80: 75: 70: 68:Étale morphism 63: 60: 29:regular scheme 9: 6: 4: 3: 2: 279: 268: 265: 263: 262:Scheme theory 260: 258: 255: 254: 252: 241: 236: 234: 229: 227: 222: 221: 215: 213: 209: 205: 200: 197: 193: 192: 188: 178: 176:9780080871509 172: 168: 167: 162: 156: 142: 138: 132: 124: 122:9780387902449 118: 114: 110: 109: 104: 98: 94: 84: 81: 79: 76: 74: 71: 69: 66: 65: 59: 57: 52: 50: 49:perfect field 46: 45:smooth scheme 42: 38: 34: 30: 26: 19: 212:expanding it 201: 186: 165: 155: 144:. Retrieved 140: 131: 107: 97: 53: 28: 22: 51:is smooth. 37:local rings 251:Categories 146:2022-02-18 89:References 163:(1980), 105:(1977), 62:See also 41:regular 173:  119:  35:whose 33:scheme 202:This 208:stub 171:ISBN 117:ISBN 39:are 27:, a 23:In 253:: 139:. 111:, 58:. 239:e 232:t 225:v 214:. 180:. 149:. 20:.

Index

regular embedding
algebraic geometry
scheme
local rings
regular
smooth scheme
perfect field
Geometrically regular ring#Examples
Étale morphism
Dimension of an algebraic variety
Glossary of scheme theory
Smooth completion
Hartshorne, Robin
Algebraic Geometry
Graduate Texts in Mathematics
ISBN
9780387902449
"Section 28.9 (02IR): Regular schemes—The Stacks project"
Demazure, Michel
Introduction to algebraic geometry and algebraic groups
ISBN
9780080871509
Stub icon
algebraic geometry
stub
expanding it
v
t
e
Categories

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑