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p-adic Teichmüller theory

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of a complex Riemann surface (an isomorphism from the upper half plane to a universal covering space of the surface) in a way that makes sense for
192: 106: 97:-adic analogue the Fuchsian uniformization of Teichmüller theory, is the study of integral Frobenius invariant indigenous bundles. 210: 184: 326: 285: 311: 89:, and the analogue of the quasi-Fuchsian condition is an integrality condition on the indigenous line bundle. So 77:
over the Riemann surface: the unique indigenous bundle that is invariant under complex conjugation and whose
321: 278: 316: 86: 66: 43: 73:-adic curves. The existence of a Fuchsian uniformization is equivalent to the existence of a canonical 39: 111: 51: 226: 188: 158: 74: 148: 138: 47: 238: 202: 170: 234: 198: 166: 221:; Rapoport, Michael (eds.), "Cohomologies p-adiques et applications arithmétiques, I.", 262: 305: 258: 35: 250: 178: 218: 214: 17: 143: 230: 162: 131:
Kyoto University. Research Institute for Mathematical Sciences. Publications
78: 183:, AMS/IP Studies in Advanced Mathematics, vol. 11, Providence, R.I.: 116: 153: 28: 129:
Mochizuki, Shinichi (1996), "A theory of ordinary p-adic curves",
85:-adic curves the analogue of complex conjugation is the 266: 50:
and their moduli. It was introduced and developed by
65:The first problem is to reformulate the Fuchsian 286: 8: 293: 279: 152: 142: 59: 55: 180:Foundations of p-adic Teichmüller theory 81:representation is quasi-Fuchsian. For 7: 247: 245: 107:Inter-universal Teichmüller theory 27:describes the "uniformization" of 14: 249: 93:-adic Teichmüller theory, the 1: 185:American Mathematical Society 265:. You can help Knowledge by 209:Mochizuki, Shinichi (2002), 177:Mochizuki, Shinichi (1999), 343: 244: 38:, generalizing the usual 144:10.2977/prims/1195145686 25:-adic Teichmüller theory 213:; Fontaine, Jean-Marc; 261:-related article is a 87:Frobenius endomorphism 52:Shinichi Mochizuki 327:Number theory stubs 42:that describes the 312:Algebraic geometry 112:Anabelian geometry 40:Teichmüller theory 274: 273: 211:Berthelot, Pierre 194:978-0-8218-1190-0 75:indigenous bundle 34:curves and their 334: 295: 288: 281: 253: 246: 241: 205: 173: 156: 146: 48:Riemann surfaces 342: 341: 337: 336: 335: 333: 332: 331: 302: 301: 300: 299: 208: 195: 176: 137:(6): 957–1152, 128: 125: 103: 12: 11: 5: 340: 338: 330: 329: 324: 322:P-adic numbers 319: 314: 304: 303: 298: 297: 290: 283: 275: 272: 271: 254: 243: 242: 206: 193: 174: 124: 121: 120: 119: 114: 109: 102: 99: 67:uniformization 44:uniformization 13: 10: 9: 6: 4: 3: 2: 339: 328: 325: 323: 320: 318: 317:Number theory 315: 313: 310: 309: 307: 296: 291: 289: 284: 282: 277: 276: 270: 268: 264: 260: 259:number theory 255: 252: 248: 240: 236: 232: 228: 225:(278): 1–49, 224: 220: 216: 212: 207: 204: 200: 196: 190: 186: 182: 181: 175: 172: 168: 164: 160: 155: 150: 145: 140: 136: 132: 127: 126: 122: 118: 115: 113: 110: 108: 105: 104: 100: 98: 96: 92: 88: 84: 80: 76: 72: 68: 63: 61: 57: 53: 49: 45: 41: 37: 33: 31: 26: 24: 19: 267:expanding it 256: 222: 219:Kato, Kazuya 215:Illusie, Luc 179: 134: 130: 94: 90: 82: 70: 64: 29: 22: 21: 15: 18:mathematics 306:Categories 223:Astérisque 154:2433/59800 123:References 231:0303-1179 163:0034-5318 79:monodromy 117:nilcurve 101:See also 239:1922823 203:1700772 171:1437328 54: ( 237:  229:  201:  191:  169:  161:  36:moduli 257:This 32:-adic 263:stub 227:ISSN 189:ISBN 159:ISSN 60:1999 56:1996 149:hdl 139:doi 62:). 46:of 16:In 308:: 235:MR 233:, 217:; 199:MR 197:, 187:, 167:MR 165:, 157:, 147:, 135:32 133:, 58:, 20:, 294:e 287:t 280:v 269:. 151:: 141:: 95:p 91:p 83:p 71:p 30:p 23:p

Index

mathematics
p-adic
moduli
Teichmüller theory
uniformization
Riemann surfaces
Shinichi Mochizuki
1996
1999
uniformization
indigenous bundle
monodromy
Frobenius endomorphism
Inter-universal Teichmüller theory
Anabelian geometry
nilcurve
doi
10.2977/prims/1195145686
hdl
2433/59800
ISSN
0034-5318
MR
1437328
Foundations of p-adic Teichmüller theory
American Mathematical Society
ISBN
978-0-8218-1190-0
MR
1700772

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