Bulletin of the American Mathematical Society

Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Bernadette Perrin-Riou
Title: -Adic -functions and -adic representations
Additional book information: translated by Leila Schneps, Amer. Math. Soc., Providence, RI, 2000, xx + 150 pp., ISBN 0-8218-1946-1, $49.00$

[BK]

Bloch, S., Kato, K.: -functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift (Vol. I), P. Cartier, et al., eds., Prog. in Math. 86, Boston: Birkhäuser (1990) 333-400. MR 1086888

[BCDT]

Breuil, C., Conrad, B., Diamond, F., Taylor, R.: On the modularity of elliptic curves over : wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), 843-939.

[CW]

Coates, J., Wiles, A.: On -adic -functions and elliptic units, J. Austral. Math. Soc. (ser. A) 26 (1978) 1-25. MR 0510581

[Cn]

Coleman, R.: Division values in local fields, Invent. Math. 53 (1979) 91-116. MR 0560409

[Cz]

Colmez, P.: Théorie d'Iwasawa des représentations de de Rham d'un corps local, Ann. of Math. 148 (1998) 485-571. MR 1668555

[Gr]

Greenberg, R.: Iwasawa theory for -adic representations, in: Algebraic number theory in honor of K. Iwasawa, J. Coates et al., eds., Adv. Stud. in Pure Math. 17, Boston: Academic Press (1989) 97-137. MR 1097613

[La]

Lang, S.: Cyclotomic fields I and II, Graduate Texts in Math. 121, New York: Springer-Verlag (1990) 397-419. MR 1029028

[PR1]

Perrin-Riou, B.: Théorie d'Iwasawa des représentations -adiques sur un corps local, Invent. Math. 115 (1994) 81-149. MR 1248080

[PR2]

-: La fonction -adique de Kubota-Leopoldt, in: Arithmetic Geometry, Contemp. Math. 174 (1994) 61-93. MR 1299735

[PR3]

-: Fonctions -adiques d'une courbe elliptique et points rationnels, Ann. Inst. Fourier 43 (1993) 945-995. MR 1252935

[Ru1]

Rubin, K.: The main conjecture. Appendix to: Cyclotomic fields I and II, S. Lang, Graduate Texts in Math. 121, New York: Springer-Verlag (1990) 397-419. MR 1029028

[Ru2]

-: Euler Systems. Annals of Math. Studies 147, Princeton: Princeton University Press (2000). MR 1749177

[Wi]

Wiles, A.: Modular elliptic curves and Fermat's Last Theorem, Annals of Math. 141 (1995), 443-551. MR 1333035

[BK]

Bloch, S., Kato, K.: -functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift (Vol. I), P. Cartier, et al., eds., Prog. in Math. 86, Boston: Birkhäuser (1990) 333-400. MR 1086888

[BCDT]

Breuil, C., Conrad, B., Diamond, F., Taylor, R.: On the modularity of elliptic curves over : wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), 843-939.

[CW]

Coates, J., Wiles, A.: On -adic -functions and elliptic units, J. Austral. Math. Soc. (ser. A) 26 (1978) 1-25. MR 0510581

[Cn]

Coleman, R.: Division values in local fields, Invent. Math. 53 (1979) 91-116. MR 0560409

[Cz]

Colmez, P.: Théorie d'Iwasawa des représentations de de Rham d'un corps local, Ann. of Math. 148 (1998) 485-571. MR 1668555

[Gr]

Greenberg, R.: Iwasawa theory for -adic representations, in: Algebraic number theory in honor of K. Iwasawa, J. Coates et al., eds., Adv. Stud. in Pure Math. 17, Boston: Academic Press (1989) 97-137. MR 1097613

[La]

Lang, S.: Cyclotomic fields I and II, Graduate Texts in Math. 121, New York: Springer-Verlag (1990) 397-419. MR 1029028

[PR1]

Perrin-Riou, B.: Théorie d'Iwasawa des représentations -adiques sur un corps local, Invent. Math. 115 (1994) 81-149. MR 1248080

[PR2]

-: La fonction -adique de Kubota-Leopoldt, in: Arithmetic Geometry, Contemp. Math. 174 (1994) 61-93. MR 1299735

[PR3]

-: Fonctions -adiques d'une courbe elliptique et points rationnels, Ann. Inst. Fourier 43 (1993) 945-995. MR 1252935

[Ru1]

Rubin, K.: The main conjecture. Appendix to: Cyclotomic fields I and II, S. Lang, Graduate Texts in Math. 121, New York: Springer-Verlag (1990) 397-419. MR 1029028

[Ru2]

-: Euler Systems. Annals of Math. Studies 147, Princeton: Princeton University Press (2000). MR 1749177

[Wi]

Wiles, A.: Modular elliptic curves and Fermat's Last Theorem, Annals of Math. 141 (1995), 443-551. MR 1333035