Talk:Karl Rubin

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[edit] Papers section

SOURCE: http://www.math.uci.edu/~krubin/rubincv.pdf Need to fix each citation according to Wikipedia standard

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1. Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Inventiones Mathematicae 64, (1981) 455–470.
2. Iwasawa theory and elliptic curves: supersingular primes. In: Journ´ees Arithmetiques 1980, London Math. Soc. Lect. Notes 56, Cambridge: Cambridge University Press (1982) 379–383.
3. (with A. Wiles) Mordell-Weil groups of elliptic curves over cyclotomic fields. In: Number Theory related to Fermat’s last theorem, Progress in Math. 26, Boston: Birkhauser (1982) 237–254.
4. Congruences for special values of L-functions of elliptic curves with complex multiplication, Inventiones math. 71 (1983) 339–364.
5. Elliptic curves and Zp-extensions, Compositio math. 56 (1985) 237–250.
6. p-adic L-functions and descent on non-CM elliptic curves. In: Number Theory (proceedings of a conference in Montreal, 1985), Canadian Math. Soc. Conf. Proc. 7, Providence: American Math. Soc. (1987) 405–419.
7. Local units, elliptic units, Heegner points, and elliptic curves, Inventiones math. 88 (1987) 405–422.
8. Descents on elliptic curves with complex multiplication. In: S´eminaire de Th´eorie des Nombres, Paris 1985-86, Progress in Math. 71, Boston: Birkhauser (1988) 165–174.
9. Global units and ideal class groups, Inventiones math. 89 (1987) 511–526.
10. Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Inventiones math. 89 (1987) 527–560.
11. Tate-Shafarevich groups of elliptic curves with complex multiplication. In: Algebraic number theory in honor of K. Iwasawa, Advanced Studies in Pure Math. 17, Academic Press (1989) 409–419.
12. On the main conjecture of Iwasawa theory for imaginary quadratic fields, . Inventiones math. 93 (1988) 701–713
13. The work of Kolyvagin on the arithmetic of elliptic curves. In: Arithmetic of Complex Manifolds, Barth and Lange, eds. Lecture Notes in Math. 1399, New York: Springer (1989) 128–136.
14. The main conjecture. Appendix to: Cyclotomic Fields I and II by S. Lang, Graduate Texts in Math. 121, New York: Springer (1990) 397–419.
15. Kolyvagin’s system of Gauss sums. In: Arithmetic Algebraic Geometry, van der Geer, Oort and Steenbrink, eds. Progress in Math. 89, Boston: Birkhauser (1991) 309–324.
16. The one-variable main conjecture for elliptic curves with complex multiplication. In: L-functions in arithmetic, London Math. Soc. Lect. Notes 153, Cambridge University Press (1991) 353–371.
17. The “main conjectures” of Iwasawa theory for imaginary quadratic fields, Inventiones math. 103 (1991) 25–68.
18. Stark units and Kolyvagin’s “Euler systems”, J. f¨ur die reine und angew. Math. 425 (1992) 141–154.
19. p-adic L-functions and rational points on elliptic curves with complex multiplication, Inventiones math. 107 (1992) 323–350.
20. p-adic variants of the Birch and Swinnerton-Dyer conjecture. In: p-adic monodromy and the Birch and Swinnerton-Dyer Conjecture, Mazur and Stevens, eds. Contemporary Mathematics 165, Providence: Amer. Math. Soc. (1994) 71–80.
21. More “main conjectures” for imaginary quadratic fields. In: Elliptic curves and related topics, Kisilevsky and Murty, eds. CRM Proceedings and Lecture Notes 4, Providence: Amer. Math. Soc. (1994) 23–28.
22. Abelian varieties, p-adic heights and derivatives. In: Algebra and Number Theory (Essen, December 1992), Frey and Ritter, eds. Berlin: de Gruyter (1994) 247–266.
23. (with A. Silverberg) A report on Wiles’ Cambridge lectures, Bull. Amer. Math. Soc. (1994) 15–38.
24. (with A. Silverberg) Families of elliptic curves with constant mod p representations. In: Elliptic curves, modular forms, and Fermat’s Last Theorem (Hong Kong, December 1994), Coates and Yau, eds. Cambridge: International Press (1995) 148–161.
25. A Stark conjecture “over Z” for abelian L-functions with multiple zeros, Annales de l’Institut Fourier 46 (1996) 33–62.
26. Euler systems and exact formulas in number theory, Jahresbericht der Deutschen Math.-Verein. 98 (1996) 30–39.
27. Modularity of mod 5 representations. In: Modular forms and Fermat’s Last Theorem, Cornell, Silverman, and Stevens, eds. New York: Springer (1997) 463–474.
28. (with B. de Smit and R. Schoof) Criteria for complete intersections. In: Modular forms and Fermat’s Last Theorem, Cornell, Silverman, and Stevens, eds. New York: Springer (1997) 343–355.
29. (with A. Silverberg) Mod 6 representations of elliptic curves. In: Automorphic forms, automorphic representations, and arithmetic, Doran, Dau, and Gilbert, eds. Proc. Symp. Pure Math. 66, Providence: American Math. Soc. (1999) 213–220.
30. Euler systems and modular elliptic curves. In: Galois representations in arithmetic algebraic geometry, Scholl and Taylor, eds. London Math. Soc. Lect. Notes 254, Cambridge: Cambridge University Press (1998) 351–367.
31. Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer. In: Arithmetic theory of elliptic curves (Cetraro, Italy 1997), C. Viola, ed. Lecture Notes in Math. 1716, New York: Springer (1999) 167–234.
32. (with C. Greither, D. Replogle, and A. Srivastav) Swan modules and Hilbert-Speiser number fields, Journal of Number Theory 79 (1999) 164–173.
33. (with A. Silverberg) Ranks of elliptic curves in families of quadratic twists, Experimental Mathematics 9 (2000) 583–590.
34. (with A. Silverberg) Mod 2 representations of elliptic curves, Proc. Amer. Math. Soc. 129 (2001) 53–57
35. (with A. Silverberg) Rank frequencies for quadratic twists of elliptic curves, Experimental Mathematics 10 (2001) 559–569.
36. (with B. Mazur) Elliptic curves and class field theory. In: Proceedings of the International Congress of Mathematicians, ICM 2002, Beijing, Ta Tsien Li, ed., vol. II. Beijing: Higher Education Press (2002) 185–195.
37. (with A. Silverberg) Supersingular abelian varieties in cryptology. In: Advances in Cryptology — CRYPTO 2002, M. Yung, ed., Lect. Notes in Computer Science 2442, New York: Springer (2002) 336–353.
38. (with A. Silverberg) Ranks of elliptic curves, Bull. Amer. Math. Soc. 39 (2002) 455–474.
39. (with A. Silverberg) Torus-based cryptography. In: Advances in Cryptology — CRYPTO 2003, D. Boneh, ed., Lect. Notes in Computer Science 2729, New York: Springer (2003) 349–365.
40. (with B. Mazur) Studying the growth of Mordell-Weil. In: Documenta math. Extra Volume: Kazuya Kato’s Fiftieth Birthday (2003) 585–607.
41. (with B. Mazur) Kolyvagin systems. Memoirs of the AMS 168, number 799 (2004) 96pp.
42. (with B. Mazur) Pairings in the arithmetic of elliptic curves. In: Modular Curves and Abelian Varieties, J. Cremona et al., eds., Progress in Math. 224, Basel: Birkha¨user (2004) 151–163.
43. (with R. Pollack) The main conjecture for CM elliptic curves at supersingular primes. Annals of Math. (2) 159 (2004) 447–464.
44. Right triangles and elliptic curves. In: Mathematical Adventures for Students and Amateurs, D. Hayes and T. Shubin, eds., Mathematical Assn. of America (2004) 73–80.
45. (with B. Mazur) Introduction to Kolyvagin systems. In: Stark’s Conjectures: Recent Work and New Directions, Contemp. Math. 358, Providence: Amer. Math. Soc. (2004) 207–221.
46. (with A. Silverberg) Algebraic tori in cryptography. In: High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams, Fields Institute Communications Series 41, Providence: Amer. Math. Soc. (2004) 317–326.
47. (with A. Silverberg) Using primitive subgroups to do more with fewer bits. In: Algorithmic Number Theory (ANTS VI), Lect. Notes in Computer Science 3076, New York: Springer (2004) 18–41.
48. (with M. van Dijk, R. Granger, D. Page, A. Silverberg, M. Stam, and D. Woodruff) Practical cryptography in high dimensional tori. In: Advances in Cryptology — EUROCRYPT 2005, R. Cramer, ed., Lect. Notes in Computer Science 3494, New York: Springer (2005) 234–250.
49. (with B. Mazur) Organizing the arithmetic of elliptic curves. Advances in Mathematics 198 (2005) 504–546.
50. (with B. Mazur) Finding large Selmer groups. Journal of Differential Geometry 70 (2005) 1–22.
51. Appendix to: Anticyclotomic Iwasawa theory of CM elliptic curves, by A. Agboola and B. Howard. Annales de l’Institut Fourier. 56 (2006) 1001–1048. Preprints
52. Fudge factors in the Birch and Swinnerton-Dyer conjecture. To appear in Ranks of elliptic curves and random matrix theory, Conrey et al., eds., Cambridge University Press.
53. (with A. Silverberg) Twists of elliptic curves of rank at least four. To appear in Ranks of elliptic curves and random matrix theory, Conrey et al., eds., Cambridge University Press.
54. (with B. Mazur) Finding large Selmer rank via an arithmetic theory of local constants. To appear in Annals of Mathematics. http://arxiv.org/math/0512085
55. (with B. Mazur and A. Silverberg) Twisting commutative algebraic groups. To appear. http://arxiv.org/math/0609066 updated October 2, 2006

Timothy Clemans 09:23, 7 December 2006 (UTC)