On isomorphism problems on universal deformation rings and universal modular deformation rings for residual modular Galois representations

• Project/Area Number: 21740031
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Kyoto Sangyo University
• Principal Investigator: YAMAGAMI Atsushi Kyoto Sangyo University, 理学部, 准教授 (00440876)
• Project Period (FY): 2009 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: p-進保型形式 / ヘッケ環 / ガロア表現

Research Abstract

In the p-supersingular case, I constructed p-adic analytic families of elliptic eigenforms of infinite slope. Also, in the p-supercuspidal case, I proved that it is impossible to construct any p-adic analytic family of elliptic eigenforms of infinite slope by the base change theory with p-adic analytic families of Hilbert eigenforms of finite slope, or the Jacquet-Langlands correspondence with automorphic forms on definite quaternion algebras.

Research Products

• [Presentation] On p-adic automorphic forms on definite quaternion algebras (2011)
  • Author(s): 山上敦士
  • Organizer: 九州代数的整数論2011
  • Place of Presentation: 九州大学
  • Year and Date: 2011-02-19
• [Presentation] On p-adic families of eigenforms of infinite slope (2010)
  • Author(s): 山上敦士
  • Organizer: 数論幾何学ワークショップ2010
  • Place of Presentation: 沖縄県
  • Year and Date: 2010-08-26
• [Presentation] On p-adic families of eigenforms of infinte slope (2010)
  • Author(s): 山上敦士
  • Organizer: 数論幾何学ワークショップ2010
  • Place of Presentation: 沖縄県那覇市
  • Year and Date: 2010-08-06
• [Presentation] On p-adic analytic families of eigenforms of infinite slope (2009)
  • Author(s): 山上敦士
  • Organizer: 第4回福岡数論研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2009-08-26
• [Presentation] On p-adic analytic families of eigenforms of infinite slope (2009)
  • Author(s): 山上敦士
  • Organizer: 福岡数論研究集会
  • Place of Presentation: 九州大学
  • Year and Date: 2009-08-26
• [Presentation] Eigencurve について (2009)
  • Author(s): 山上敦士
  • Organizer: 第17回整数論サマースクール「1進ガロア表現とガロア変形の整数論」
  • Place of Presentation: アピカルイン京都
  • Year and Date: 2009-08-21