Ir al contenido

Documat


On the elliptic stark conjecture in higherweight

  • Autores: Francesca Gatti, Xavier Guitart Árbol académico
  • Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 2, 2020, págs. 577-619
  • Idioma: inglés
  • DOI: 10.5565/publmat6422009
  • Enlaces
  • Resumen
    • We study the special values of the triple product p-adic L-function constructedby Darmon and Rotger at all classical points outside the region of interpolation.We propose conjectural formulas for these values that can be seen as extendingthe Elliptic Stark Conjecture, and we provide theoretical evidence for them by provingsome particular cases.

  • Referencias bibliográficas
    • A. O. L. Atkin and W. C. W Li, Twists of newforms and pseudo-eigenvalues ofW-operators, Invent. Math. 48(3) (1978), 221-243. DOI: 10.1007/BF01390245.
    • J. Bellaïche and M. Dimitrov, On the eigencurve at classical weight 1 points,Duke Math. J. 165(2) (2016), 245-266. DOI: 10.1215/00127094-3165755
    • M. Bertolini, F. Castella, H. Darmon, S. Dasgupta, K. Prasanna, andV. Rotger, p-adic L-functions and Euler systems: a tale in two trilogies,...
    • M. Bertolini and H. Darmon, Kolyvagin's descent and Mordell-Weil groupsover ring class _elds, J. Reine Angew. Math. 1900(412) (1990),...
    • M. Bertolini, H. Darmon, and K. Prasanna, Generalized Heegner cycles andp-adic Rankin L-series, With an appendix by Brian Conrad, Duke Math....
    • M. Bertolini, H. Darmon, and K. Prasanna, Chow-Heegner points on CMelliptic curves and values of p-adic L-functions, Int. Math. Res. Not....
    • M. Bertolini, H. Darmon, and K. Prasanna, p-adic L-functions and theconiveau _ltration on Chow groups, With an appendix by Brian Conrad, J....
    • M. Bertolini, M. A. Seveso, and R. Venerucci, Reciprocity laws for balanceddiagonal classes, submitted to the collective volume \Heegner Points,...
    • A. Betina, M. Dimitrov, and A. Pozzi, On the failure of Gorensteinness atweight 1 Eisenstein points of the eigencurve, Preprint (2018). arXiv:1804.00648.
    • I. Blanco-Chac_on and M. Fornea, Twisted triple product p-adic L-functionsand Hirzebruch-Zagier cycles, J. Inst. Math. Jussieu, Published...
    • D. Casazza and V. Rotger, On the elliptic Stark conjecture at primes ofmultiplicative reduction, Indiana Univ. Math. J. 68(4) (2019), 1233-1253.DOI:...
    • F. Castella, On the exceptional specializations of big Heegner points, J. Inst.Math. Jussieu 17(1) (2018), 207-240. DOI: 10.1017/S1474748015000444.
    • F. Castella. On the p-adic variation of Heegner points, J. Inst. Math. Jussieu,Published online (2019). DOI: 10.1017/S1474748019000094.
    • H. Darmon, A. Lauder, and V. Rotger, Stark points and p-adic iteratedintegrals attached to modular forms of weight one, Forum Math. Pi 3 (2015),e8,...
    • H. Darmon and V. Rotger, Diagonal cycles and Euler systems I: A p-adicGross-Zagier formula, Ann. Sci. _ Ec. Norm. Supér. (4) 47(4) (2014),...
    • H. Darmon and V. Rotger, Stark-Heegner points and diagonal classes, andp-adic families of diagonal cycles, submitted to the collective volume...
    • F. Gatti, X. Guitart, M. Masdeu, and V. Rotger, Special values of tripleproductp-adic L-functions and non-crystalline diagonal classes, Preprint...
    • E. Ghate, Ordinary forms and their local Galois representations, in: \Alge-bra and Number Theory", Hindustan Book Agency, Delhi, 2005,...
    • B. H. Gross, \Arithmetic on Elliptic Curves with Complex Multiplication",With an appendix by B. Mazur, Lecture Notes in Mathematics 776,...
    • B. H. Gross and D. B. Zagier, Heegner points and derivatives of L-series,Invent. Math. 84(2) (1986), 225-320. DOI: 10.1007/BF01388809.
    • B. Howard, Variation of Heegner points in Hida families, Invent. Math. 167(1)(2007), 91-128. DOI: 10.1007/s00222-006-0007-0.
    • M.-L. Hsieh, Hida families and p-adic triple product L-functions, Amer. J.Math. (to appear).
    • U. Jannsen, \Mixed Motives and Algebraic K-Theory", With appendices byS. Bloch and C. Schoen, Lecture Notes in Mathematics 1400, Springer-Verlag,Berlin,...
    • N. A. Karpenko, Weil transfer of algebraic cycles, Indag. Math. (N.S.) 11(1)(2000), 73-86. DOI: 10.1016/S0019-3577(00)88575-4
    • N. M. Katz, p-adic interpolation of real analytic Eisenstein series, Ann. ofMath. (2) 104(3) (1976), 459-571. DOI: 10.2307/1970966.
    • V. A. Kolyvagin, Euler systems, in: \The Grothendieck Festschrift", Vol. II,Progr. Math. 87, Birkhäuser Boston, Boston, MA, 1990, pp....
    • D. Loeffler, C. Skinner, and S. Zerbes, Euler systems for GSp(4), J. Eur.Math. Soc. (JEMS) (to appear).
    • D. Loeffler, C. Skinner, and S. L. Zerbes, Syntomic regulators of Asai-Flachclasses, in: \Development of Iwasawa Theory | the Centennial of...
    • J. Nekov_a_r, Kolyvagin's method for Chow groups of Kuga-Sato varieties, In-vent. Math. 107(1) (1992), 99-125. DOI: 10.1007/BF01231883.
    • J. Nekov_a_r, On the p-adic height of Heegner cycles, Math. Ann. 302(4) (1995),609-686. DOI: 10.1007/BF01444511.
    • I. Piatetski-Shapiro and S. Rallis, Rankin triple L functions, CompositioMath. 64(1) (1987), 31-115.
    • N. Schappacher, \Periods of Hecke Characters", Lecture Notes in Mathematics1301, Springer-Verlag, Berlin, 1988. DOI: 10.1007/BFb0082094.
    • A. J. Scholl, Motives for modular forms, Invent. Math. 100(2) (1990), 419-430.DOI: 10.1007/BF01231194.
    • A. J. Scholl, Classical motives, in: \Motives", Part 1 (Seattle,WA, 1991), Proc.Sympos. Pure Math. 55, Amer. Math. Soc., Providence, RI,...
    • S. Zhang, Heights of Heegner cycles and derivatives of L-series, Invent. Math.130(1) (1997), 99-152. DOI: 10.1007/s002220050179.
    • S. Zhang, Heights of Heegner points on Shimura curves, Ann. of Math. (2)153(1) (2001), 27-147. DOI: 10.2307/2661372.

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno