Diophantine Geometry: An IntroductionThis is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises. |
Contents
VI | 6 |
VII | 8 |
VIII | 9 |
IX | 15 |
X | 22 |
XI | 24 |
XII | 34 |
XIV | 37 |
LXIII | 267 |
LXIV | 273 |
LXV | 279 |
LXVI | 283 |
LXVII | 290 |
LXVIII | 299 |
LXIX | 300 |
LXX | 304 |
XV | 44 |
XVI | 49 |
XVIII | 52 |
XIX | 56 |
XX | 67 |
XXI | 68 |
XXII | 70 |
XXIII | 74 |
XXIV | 76 |
XXV | 81 |
XXVI | 84 |
XXVII | 91 |
XXVIII | 93 |
XXIX | 97 |
XXX | 103 |
XXXI | 110 |
XXXIII | 111 |
XXXIV | 113 |
XXXV | 116 |
XXXVI | 119 |
XXXVIII | 121 |
XXXIX | 128 |
XL | 134 |
XLII | 138 |
XLIII | 142 |
XLIV | 151 |
XLVI | 159 |
XLVII | 160 |
XLVIII | 162 |
XLIX | 168 |
L | 170 |
LI | 174 |
LII | 183 |
LIII | 195 |
LIV | 199 |
LV | 210 |
LVI | 224 |
LVII | 237 |
LVIII | 241 |
LIX | 243 |
LX | 251 |
LXI | 257 |
LXII | 260 |
LXXI | 307 |
LXXII | 316 |
LXXIII | 323 |
LXXIV | 329 |
LXXV | 341 |
LXXVI | 345 |
LXXVII | 353 |
LXXVIII | 361 |
LXXIX | 367 |
LXXX | 369 |
LXXXI | 373 |
LXXXII | 379 |
LXXXIII | 381 |
LXXXIV | 385 |
LXXXV | 389 |
LXXXVI | 393 |
LXXXVII | 401 |
LXXXVIII | 408 |
LXXXIX | 412 |
XC | 418 |
XCI | 421 |
XCII | 428 |
XCIII | 433 |
XCIV | 434 |
XCVI | 439 |
XCVII | 443 |
XCVIII | 444 |
XCIX | 445 |
C | 451 |
CI | 456 |
CII | 457 |
CIII | 465 |
CIV | 472 |
CV | 474 |
CVI | 475 |
CVII | 479 |
CVIII | 482 |
CIX | 487 |
CX | 497 |
| 504 | |
CXII | 520 |
| 527 | |
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Common terms and phrases
abc conjecture abelian variety absolute value affine variety algebraic number ample divisor arithmetic associated birational canonical height Cartier divisor coefficients completes the proof compute conjecture constant coordinates curve of genus definition degree denote Diophantine divisor class effective divisor elliptic curve embedding equation equivalent estimate example Exercise Faltings fiber finite set formula function field genus g gives height function Hence homogeneous homomorphism hyperplane ideal implies integer irreducible isomorphic Jac(C Jacobian Let f line bundle linear system linearly equivalent lower bound Mordell-Weil morphism Néron model nonzero notation number field open subset polynomial projective variety properties Proposition Prove rational function rational map rational points Riemann form ring Roth's theorem satisfying sheaf Siegel's smooth projective curve subvariety theory theta function unramified variety defined variety of dimension vector space Vojta's inequality Zariski
Popular passages
Page 4 - The heavens rejoice in motion, why should I Abjure my so much lov'd variety.
Page 3 - have appeared in the literature. A list of comments and citations for the exercises will be found at the end of the book. Exercises marked with a single asterisk are somewhat more difficult, and two asterisks signal an unsolved problem. Standard Notation Throughout this book, we use the symbols Z, Q,
Page 3 - C, Fq, and Z¿ to represent the integers, rational numbers, real numbers, complex numbers, field with q elements, and p-adic integers, respectively. Further, if R is any ring, then R” denotes the group of invertible elements of R; and if A is an abelian group, then Am