Open Problems In Mathematics Nash Pdf

Reprints and preprints

by René Schoof

(with L. Washington and M. Mishra) Class groups of real cyclotomic fields , Monatshefte für Mathematik, 195 (2021), 489–496. (pdf)
On the ideal class group of the normal closure of Q(n^1/p ), Journal of Number Theory 216 (2020), 69–82. (pdf)
(with P. Mercuri) Modular forms invariant under non-split Cartan subgroups, Math. Comp. 89 (2020), 1969– 1991. (pdf).
Heights and principal ideals of certain cyclotomic fields, in Eds Chakraborty et al: "Class groups of number fields and related topics", Springer Verlag 2020, 89–96. (pdf).
De vervloekte kromme, Nieuw Archief voor wiskunde, 5/20 (2019), 131–134. (pdf).
Is a finite locally free group scheme killed by its order?, in Ed. Oort, F.: "Open problems in algebraic geometry", Advanced Lectures in Math. 46, International Press, ISBN 978-7-04-050831-4, Beijing 2018, 1–7. (pdf).
The discrete logarithm problem, in Eds. Nash, J. and Rassias, M.: "Open problems in mathematics", Springer Verlag 2016, 403–416. (pdf).
(with V. Dose, J. Fernández, J. González) The automorphism group of the non-split Cartan modular curve of level 11, Journal of Algebra 417 (2014), 95–102. (pdf).
On the modular curve X₀(23) , "Geometry and Arithmetic", EMS Publishing House, Zürich 2012, 317–345. (pdf)
(with N. Tzanakis) Integral points of a modular curve of level 11, Acta Arithmetica 152 (2012), 39–49. (pdf)
Semistable abelian varieties with good reduction outside 15, Manuscripta Mathematica, 139 (2012), 49–70. (pdf)
(with L.C. Washington) Visibility of ideal classes, Journal of Number Theory 130 (2010), 2715–2731. (pdf)
Catalan's Conjecture, Universitext, Springer Verlag, (Google books), ISBN 978-1-84800-184-8. London 2008.
Four primality testing algorithms, "Algorithmic number theory" MSRI Publications 44, Cambridge University Press, Cambridge 2008, 101–126. (pdf, errata)
Computing Arakelov class groups, "Algorithmic number theory" MSRI Publications 44, Cambridge University Press, Cambridge 2008, 447–495. (pdf) (errata)
(with M. Larsen) A refined counter-example to the support conjecture for abelian varieties, J. of Number Theory 116 (2006), 396–398. (pdf)
Abelian varieties over Q with bad reduction in one prime only, Compositio Math. 141 (2005), 847–868. (pdf) (errata)
(with E. Bayer-Fluckiger, M. Monsurrò, R. Parimala) Trace forms of G-Galois algebras in virtual cohomological dimension 1 and 2, Pacific J. of Math. 217 (2004), 29–43. (pdf)
Abelian varieties over cyclotomic fields with good reduction everywhere, Math. Annalen. 325 (2003), 413–448. (pdf, errata)
Class groups of real cyclotomic fields of prime conductor, Math. Comp. 72 (2003), 913–937. (pdf) (errata).
(with J.-C. Lario) Computations with Hecke rings and deformation rings, J. of Experimental Math. 11 (2002), 303–312. (pdf)
Abelian varieties with good reduction everywhere over Q(√6), p. 287–306 in "Class Field Theory — Its Centenary and Prospect" (ed. by K. Miyake), Advanced Studies in Pure Mathematics , Math. Soc. Japan, Tokyo 2001. (pdf)
Finite flat group schemes over Artin rings, Compositio Math. 128 (2001), 1–15. (pdf)
Abelian varieties over the field of the 20th roots of unity with good reduction everywhere, p. 291–296 in Ciliberto, C. et al., Proceedings of the NATO advanced research workshop "Applications of Algebraic Geometry to Coding Theory, Physics and Computation", Kluwer, Dordrecht 2001. (pdf)
(with G. van der Geer) Effectivity of Arakelov divisors and the analogue of the theta divisor of a number field, Selecta Math. New Ser. 6 (2000), 377–398. (pdf)
Algebraic number theory, pp. 23–32 in: C. Andradas and C. Corrales Rodrigáñez (eds.): "400 años de matemáticas en torno al último teorema de Fermat", Editorial de la Universidad Complutense de Madrid, 1999. ISBN: 84-89784-38-8. (pdf)
Minus class groups of cyclotomic fields of prime conductor, Math. Comp. 67 (1998), 1225–1245. (pdf)
(with B. de Smit and K. Rubin) Criteria for complete intersections, pp.343–355 in: G. Cornell, J. Silverman, G. Stevens (eds.), "Modular Forms and Fermat's Last Theorem", Springer Verlag, New York 1997. (pdf)
(with C. Corrales Rodrigáñez) The support problem and its elliptic analogue, Journal of Number Theory 64 (1997), 276–290. ( pdf) (erratum)
(with N. Schappacher) Beppo Levi and the arithmetic of elliptic curves, The Mathematical Intelligencer 18 (1996), 57–69. (pdf)
Wiles's proof of the Taniyama-Weil conjecture for semi-stable elliptic curves over Q, Gazette de Mathématiques 66 (1995), 7–24. Reprinted in Kantor, J.M. (ed): Où sont les Mathématiques?, Société Math. de France, Vuibert, Paris 2002, 305–326. (pdf)
Fermat's Last Theorem, pp. 193–211 in: "Überblicke Mathematik", Jahrbuch 1995, Vieweg-Verlag 1995. ISBN 3-528-06607-5. (pdf)
Families of curves and weight distributions of codes, Bulletin AMS. 32 (1995), 171–183. (pdf)
(with J.S. Kraft) Computing Iwasawa invariants of real quadratic number fields, Compositio Math. 97 (1995), 135–155. (pdf) (errata).
Counting points on elliptic curves over finite fields, in: "Les 18ièmes Journées Arithmétiques, Bordeaux 1993", J. Théorie de Nombres Bordeaux 7 (1995), 219–254. (pdf) (errata).
Algebraic curves over F ₂ with many rational points, Journal of Number Theory 41 (1992), 6–14. (pdf)
(with G. van der Geer and M. van der Vlugt) Weight formulas for ternary Melas codes, Math. Comp. 58, (1992), 781–792. (JSTOR pdf)
(with M. van der Vlugt) Hecke operators and the weight distributions of certain codes, Journal of Combinatorial Theory A, 57, (1991), 163–186. pdf)
The exponents of the groups of points on the reductions of an elliptic curve , pp. 325–336 in: G. van der Geer, "Arithmetic Algebraic Geometry", Progress in Math. 89 , Birkhäuser, New York 1991. ISBN 0-8176-3513-0 (pdf)
Algebraic curves and coding theory, Università di Trento 1990. Preprint 336, 38 pages. (in pdf format)
The structure of minus class groups of abelian number fields, pp. 185–204 in: C. Goldstein (ed.), "Séminaire de Théorie de Nombres, Paris 1988–1990", Progress in Math. 91, Birkhäuser 1990, 185–204. (scan).
(with L.C. Washington) Quintic polynomials and real cyclotomic fields with large class numbers, Math. Comp. 50, (1988), 543–556. (JSTOR pdf).
Cohomology of class groups of cyclotomic fields; an application to Morse-Smale diffeomorphisms, J. of Pure and Applied Algebra 53, (1988), 125–137. (pdf)
Nonsingular plane cubic curves over finite fields, J. of Combinatorial Theory, series A, 46, (1987), 183–211. (scanned as pdf file)
(with H.W. Lenstra jr.) Primitive normal bases for finite fields, Math. Comp. 48, (1986), 217–231. (JSTOR pdf)
Infinite class field towers of quadratic fields, J. für die reine und angewandte Mathematik 372, (1986), 209–220. (pdf).
Elliptic curves over finite fields and the computation of square roots mod p, Math. Comp. 44, (1985), 483–494. (pdf) Errata (pdf).
(with J. van der Craats) On the normal subgroups of Rubik groups, Nieuw archief voor wiskunde 2 (1984), 267–280. (scan)
Class groups of complex quadratic fields Math. Comp. 41, (1983), 295–302. (pdf)
Quadratic fields and factorization, pp. 235–286 in: H.W. Lenstra jr. and R. Tijdeman (eds.): "Computational Methods in Number Theory,", MC-Tracts 154/155, Amsterdam 1982. (scan)