Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Mathematical Autobiography Kapitel lesen Erstes Kapitel lesen

2019 | OriginalPaper | Buchkapitel

The Mathematical Works of Andrew Wiles

verfasst von : Christopher Skinner

Erschienen in: The Abel Prize 2013-2017

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper surveys the published mathematical works of Andrew Wiles up through the time he was awarded the Abel Prize.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel First Steps
Nächstes Kapitel List of Publications for Sir Andrew J. Wiles
Literatur
1.
J. Coates and A. Wiles, Kummer’s criterion for Hurwitz numbers, Algebraic number the- ory (Kyoto Internat. Sympos., Res. Inst. Math. Sci., Univ Kyoto, Kyoto, 1976), Japan Soc. Promotion Sci., Tokyo, 1977, pp. 9–23.
2.
——, Explicit reciprocity laws, Journées Arithmétiques de Caen (Univ Caen, Caen, 1976), Soc. Math. France, Paris, 1977, pp. 7–17. Astérisque No. 41–42.
3.
——, On the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 39 (1977), no. 3, 223–251.
4.
5.
6.
7.
K. Rubin and A. Wiles, Mordell-Weil groups of elliptic curves over cyclotomic fields, Number theory related to Fermat’s last theorem (Cambridge, Mass., 1981), Progr. Math., vol. 26, Birkhäuser, Boston, Mass., 1982, pp. 237–254.CrossRef
8.
9.
10.
——, On p-adic analytic families of Galois representations, Compositio Math. 59 (1986), no. 2, 231–264.MathSciNetMATH
11.
A. Wiles, On p-adic representations for totally real fields, Ann. of Math. (2) 123 (1986), no. 3, 407–456.
12.
——, On ordinary λ-adic representations associated to modular forms, Invent. Math. 94 (1988), no. 3, 529–573.
13.
——, The Iwasawa conjecture for totally real fields, Ann. of Math. (2) 131 (1990), no. 3, 493–540.
14.
——, On a conjecture of Brumer, Ann. of Math. (2) 131 (1990), no. 3, 555–565.
15.
——, Modular forms, elliptic curves, and Fermat’s last theorem, Proceedings of the In- ternational Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994), Birkhäuser, Basel, 1995, pp. 243–245.
16.
——, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551.
17.
18.
C. Skinner and A. Wiles, Ordinary representations and modular forms, Proc. Nat. Acad. Sci. U.S.A. 94 (1997), no. 20, 10520–10527.MathSciNetMATHCrossRef
19.
A. Wiles, Twenty years of number theory, Mathematics: frontiers and perspectives, Amer. Math. Soc., Providence, RI, 2000, pp. 329–342. MR1754786
20.
C. Skinner and A. Wiles, Residually reducible representations and modular forms, Inst. Hautes Études Sci. Publ. Math. 89 (1999), 5–126 (2000).MathSciNetMATH
21.
22.
——, Nearly ordinary deformations of irreducible residual representations, Ann. Fac. Sci. Toulouse Math. (6) 10 (2001), no. 1, 185–215.
23.
A. Wiles, The Birch and Swinnerton-Dyer conjecture, The millennium prize problems, Clay Math. Inst., Cambridge, MA, 2006, pp. 31–41.MATH
24.
——, Foreword [In honour of John H. Coates on the occasion of his sixtieth birthday], Doc. Math. Extra Vol. (2006), 3–4.
25.
26.
27.
A. Snowden and A. Wiles, Bigness in compatible systems, Elliptic curves, modular forms and Iwasawa theory, Springer Proc. Math. Stat., vol. 188, Springer Cham, 2016, pp. 469–492.
28.
N. Arthaud, On Birch and Swinnerton-Dyer’s conjecture for elliptic curves with complex multiplication. I, Compositio Math. 37 (1978), no. 2, 209–232.MathSciNetMATH
29.
T. Barnet-Lamb, T. Gee, and D. Geraghty, The Sato-Tate conjecture for Hilbert modular forms, J. Amer. Math. Soc. 24(2011), no. 2, 411–469.MathSciNetMATHCrossRef
30.
T. Barnet-Lamb, T. Gee, D. Geraghty, and R. Taylor, Potential automorphy and change of weight, Ann. of Math. (2) 179 (2014), no. 2, 501–609.MathSciNetMATHCrossRef
31.
32.
D. Blasius, Hilbert modular forms and the Ramanujan conjecture, Noncommutative geometry and number theory, Aspects Math., E37, Friedr. Vieweg, Wiesbaden, 2006, pp. 35–56.
33.
C. Breuil, B. Conrad, F. Diamond, and R. Taylor, On the modularity of elliptic curves over Q : wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843–939.MathSciNetMATHCrossRef
34.
35.
L. Clozel, M. Harris, and R. Taylor, Automorphy for some l-adic lifts of automorphic mod l Galois representations, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 1–181. With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vignéras.MathSciNetMATHCrossRef
36.
37.
J. Coates, The work of Mazur and Wiles on cyclotomic fields, Bourbaki Seminar, Vol. 1980/81, Lecture Notes in Math., vol. 901, Springer, Berlin-New York, 1981, pp. 220–242.
38.
39.
40.
P. Colmez, Théorie d’Iwasawa des représentations de de Rham d’un corps local, Ann. of Math. (2) 148 (1998), no. 2, 485–571 (French).MathSciNetMATHCrossRef
41.
B. Conrad, F. Diamond, and R. Taylor, Modularity of certain potentially Barsotti-Tate Galois representations, J. Amer. Math. Soc. 12(1999), no. 2, 521–567.
42.
H. Darmon, F. Diamond, and R. Taylor, Fermat’s last theorem, Current developments in mathematics, 1995 (Cambridge, MA), Int. Press, Cambridge, MA, 1994, pp. 1–154.
43.
H. Darmon, Andrew Wiles’s marvelous proof, Notices Amer. Math. Soc. 64 (2017), no. 3, 209–216.MathSciNetMATH
44.
45.
F. Diamond, The refined conjecture of Serre, Elliptic curves, modular forms, & Fermat’s last theorem (Hong Kong, 1993), Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995, pp. 22–37.
46.
——, On deformation rings and Hecke rings, Ann. of Math. (2) 144 (1996), no. 1, 137–166.
47.
——, The Taylor-Wiles construction and multiplicity one, Invent. Math. 128 (1997), no. 2, 379–391.
48.
F. Diamond, M. Flach, and L. Guo, The Tamagawa number conjecture of adjoint motives of modular forms, Annales scientifiques de l’École Normale Supérieure 37 (2004), no. 5, 663–727.MathSciNetMATHCrossRef
49.
M. Emerton, A local-global compatibility conjecture in the p-adic Langlands programme for GL2∕Q, Pure Appl. Math. Q. 2 (2006), no. 2, Special Issue: In honor of John H. Coates., 279–393.
50.
N. Freitas, B. Le Hung, and S. Siksek, Elliptic curves over real quadratic fields are modular, Invent. Math. 201 (2015), no. 1, 159–206.MathSciNetMATHCrossRef
51.
52.
M. Harris, N. Shepherd-Barron, and R. Taylor, A family of Calabi-Yau varieties and potential automorphy, Ann. of Math. (2) 171 (2010), no. 2, 779–813.MathSciNetMATHCrossRef
53.
M. Harris, K.-W. Lan, R. Taylor, and J. Thorne, On the rigid cohomology of certain Shimura varieties, Res. Math. Sci. 3 (2016), Paper No. 37, 308pp.
54.
55.
K. Kato, Generalized explicit reciprocity laws, Adv. Stud. Contemp. Math. (Pusan) 1 (1999), 57–126. Algebraic number theory (Hapcheon/Saga, 1996).
56.
——, Generalized explicit reciprocity laws, Adv. Stud. Contemp. Math. (Pusan) 1 (1999), 57–126. Algebraic number theory (Hapcheon/Saga, 1996).
57.
——, p-adic Hodge theory and values of zeta functions of modular forms, Astérisque 295 (2004), ix, 117–290 (English, with English and French summaries). Cohomologies p-adiques et applications arithmétiques. III.
58.
59.
60.
61.
G. Kings, D. Loeffler, and S. Zerbes, Rankin-Eisenstein classes and explicit reciprocity laws, Camb. J. Math. 5 (2017), no. 1, 1–122.MathSciNetMATHCrossRef
62.
63.
——, The Fontaine-Mazur conjecture for GL2, J. Amer. Math. Soc. 22 (2009), no. 3, 641–690.
64.
S. Lang, Cyclotomic fields I and II, 2nd ed., Graduate Texts in Mathematics, vol. 121, Springer-Verlag, New York, 1990. With an appendix by Karl Rubin. MR1029028MATHCrossRef
65.
66.
B. Mazur, Deforming Galois representations, Galois groups over Q (Berkeley, CA, 1987), Math. Sci. Res. Inst. Publ., vol. 16, Springer, New York, 1989, pp. 385–437.
67.
B. Mazur and J. Tilouine, Représentations galoisiennes, différentielles de Kähler et “conjec- tures principales”, Inst. Hautes Études Sci. Publ. Math. 71 (1990) (French).
68.
S. Patrikis and R. Taylor, Automorphy and irreducibility of some l-adic representations, Compos. Math. 151 (2015), no. 2, 207–229.MathSciNetMATHCrossRef
69.
B. Perrin-Riou, Théorie d’Iwasawa des représentations p-adiques sur un corps local, Invent. Math. 115 (1994), no. 1, 81–161 (French). With an appendix by Jean-Marc Fontaine.
70.
——, Théorie d’Iwasawa et loi explicite de réciprocité, Doc. Math. 4 (1999), 219–273 (French, with English summary).
71.
72.
——, On modular representations of Gal(\(\overline {\mathbf {Q}}\)/Q) arising from modular forms, Invent. Math. 100 (1990), no. 2, 431–476.MathSciNetMATHCrossRef
73.
R. Pollack and K. Rubin, The main conjecture for CM elliptic curves at supersingular primes, Ann. of Math. (2) 159 (2004), no. 1, 447–464.MathSciNetMATHCrossRef
74.
K. Rubin, Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 64 (1981), no. 3, 455–470.MathSciNetMATHCrossRef
75.
——, Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987), no. 3, 527–559.MathSciNetMATHCrossRef
76.
77.
——, Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Arithmetic theory of elliptic curves (Cetraro, 1997), Lecture Notes in Math., vol. 1716, Springer, Berlin, 1999, pp. 167–234.
78.
——, Euler systems, Annals of Mathematics Studies, vol. 147, Princeton University Press, Princeton, NJ, 2000. Hermann Weyl Lectures. The Institute for Advanced Study.
79.
80.
P. Schneider and O. Venjakob, Coates-Wiles homomorphisms and Iwasawa cohomology for Lubin-Tate extensions, Elliptic curves, modular forms and Iwasawa theory, Springer Proc. Math. Stat., vol. 188, Springer, Cham, 2016, pp. 401–468.
81.
P. Scholze, On torsion in the cohomology of locally symmetric varieties, Ann. of Math. (2) 182 (2015), no. 3, 945–1066.
82.
J.-P. Serre, Sur les représentations modulaires de degré 2 de Gal(\(\overline {\mathbf {Q}}\)/Q), Duke Math. J. 54 (1987), no. 1 (French).
83.
C. Skinner, A note on the p-adic Galois representations attached to Hilbert modular forms, Doc. Math. 14 (2009), 241–258.MathSciNetMATH
84.
C. Skinner and E. Urban, The Iwasawa main conjectures for GL2, Invent. Math. 195(2014), no. 1, 1–277.
85.
C. Skinner, K. Rubin, B. Mazur, M. Çiperiani, C. Khare, and J. Thorne, The mathematical works of Andrew Wiles, Notices Amer. Math. Soc. 64 (2017), no. 3, 217–227.MathSciNetMATHCrossRef
86.
87.
——, l-adic representations associated to modular forms over imaginary quadratic fields. II, Invent. Math. 116 (1994), no. 1–3, 619–643.MathSciNetMATHCrossRef
88.
——, l-adic representations associated to modular forms over imaginary quadratic fields. II, Invent. Math. 116 (1994), no. 1–3, 619–643.MathSciNetMATHCrossRef
89.
90.
——, On the meromorphic continuation of degree two L-functions, Doc. Math. Extra Vol. (2006), 729–779.
91.
——, Automorphy for some l-adic lifts of automorphic mod l Galois representations. II, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 183–239.
92.
J. Thorne, On the automorphy of l-adic Galois representations with small residual image, J. Inst. Math. Jussieu 11 (2012), no. 4, 855–920. With an appendix by Robert Guralnick, Florian Herzig, Richard Taylor and Thorne.MATHCrossRef
93.
——, Automorphy lifting for residually reducible l-adic Galois representations, J. Amer. Math. Soc. 28 (2015), no. 3, 785–870.
Metadaten
Titel
The Mathematical Works of Andrew Wiles
verfasst von
Christopher Skinner
Copyright-Jahr
2019
Buch
The Abel Prize 2013-2017

Print ISBN: 978-3-319-99027-9

Electronic ISBN: 978-3-319-99028-6

Copyright-Jahr: 2019

DOI
https://doi.org/10.1007/978-3-319-99028-6_26