Iwasawa theory of Hilbert modular forms for anticyclotomic extensions without Ihara’s lemma

• Autores: Bingyong Xie
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 68, Nº. 1, 2024, págs. 41-71
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6812403
• Enlaces
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• Resumen

  • Following Bertolini and Darmon’s method, with “Ihara’s lemma” among other conditions Longo and Wang proved one divisibility of the Iwasawa main conjecture for Hilbert modular forms of weight 2 and general low even parallel weight in the anticyclotomic setting respectively. In this paper, we remove the “Ihara’s lemma” condition in their results.

• Referencias bibliográficas
  • M. Bertolini and H. Darmon, Iwasawa’s Main Conjecture for elliptic curves over anticyclotomic Zp-extensions, Ann. of Math. (2) 162(1) (2005),...
  • S. Bosch, W. Lutkebohmert, and M. Raynaud ¨ , N´eron Models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics...
  • H. Carayol, Sur les repr´esentations l-adiques associ´ees aux formes modulaires de Hilbert, Ann. Sci. Ecole Norm. Sup. (4) ´ 19(3) (1986),...
  • C. Cheng, Ihara’s lemma for Shimura curves, Private manuscript (2011).
  • M. Chida and M.-L. Hsieh, On the anticyclotomic Iwasawa main conjecture for modular forms, Compos. Math. 151(5) (2015), 863–897. DOI: 10.1112/S0010437X14007787
  • M. Chida and M.-L. Hsieh, Special values of anticyclotomic L-functions for modular forms, J. Reine Angew. Math. 741 (2018), 87–131. DOI: 10.1515/crelle-2015-0072.
  • F. Diamond and R. Taylor, Non-optimal levels of mod l modular representations, Invent. Math. 115(3) (1994), 435–462. DOI: 10.1007/BF01231768.
  • O. Fouquet, Dihedral Iwasawa theory of nearly ordinary quaternionic automorphic forms, Compos. Math. 149(3) (2013), 356–416. DOI: 10.1112/S0010437X...
  • G. Henniart, Une preuve simple des conjectures de Langlands pour GL(n) sur un corps padique, Invent. Math. 139(2) (2000), 439–455. DOI: 10.1007/s002220050012.
  • P.-C. Hung, On the non-vanishing mod ` of central L-values with anticyclotomic twists for Hilbert modular forms, J. Number Theory 173...
  • F. Jarvis, Level lowering for modular mod ` representations over totally real fields, Math. Ann. 313(1) (1999), 141–160. DOI: 10.1007/s002080050255
  • C.-H. Kim, R. Pollack, and T. Weston, On the freeness of anticyclotomic Selmer groups of modular forms, Int. J. Number Theory 13(6) (2017),...
  • M. Longo, Anticyclotomic Iwasawa’s Main Conjecture for Hilbert modular forms, Comment. Math. Helv. 87(2) (2012), 303–353. DOI: 10.4171/CMH/255.
  • Manning and J. Shotton, Ihara’s Lemma for Shimura curves over totally real fields via patching, Math. Ann. 379(1-2) (2021), 187–234. DOI:...
  • J. Nekova´rˇ, Level raising and anticyclotomic Selmer groups for Hilbert modular forms of weight two, Canad. J. Math. 64(3) (2012), 588–668....
  • R. Pollack and T. Weston, On anticyclotomic µ-invariants of modular forms, Compos. Math. 147(5) (2011), 1353–1381. DOI: 10.1112/S0010437X11005318.
  • R. Taylor, On Galois representations associated to Hilbert modular forms, Invent. Math. 98(2) (1989), 265–280. DOI: 10.1007/BF01388853.
  • H. Wang, Anticyclotomic Iwasawa theory for Hilbert modular forms, Thesis (Ph.D.)-The Pennsylvania State University (2015)