Talk:Karl Rubin

Papers section
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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)