Papers

主要な参考文献：

[DK1] Samit Dasgupta and Mahesh Kakde. “On the Brumer-Stark conjecture”. preprint.

[DK2] Samit Dasgupta and Mahesh Kakde. “On Constant terms of Eisenstein Series”. Acta Arith. 200 (2):119–147, 2021.

[DK3] Samit Dasgupta and Mahesh Kakde. “Brumer-Stark units and Hilbert's 12th Problem”. preprint.

[Sil] Jesse Silliman. “Group Ring Valued Hilbert Modular Forms”. preprint.

各講演の参考文献：

栗原 将人, "Overview":

• [DK1], [DK3]

• John Tate. “Les Conjectures de Stark sur les Fonctions L d'Artin en s=0”. Progress in Mathematics. 47, Birkhaeuser (1998).

• Masato Kurihara. “Notes on the dual of the ideal class groups of CM-fields”. J. Théor. Nombr. Bordeaux. 33: 971–996, 2021.

• Ryotaro Sakamoto. “On the theory of Kolyvagin systems of rank 0.” J. Théor. Nombr. Bordeaux. 33: 1077–1102, 2021.

片岡 武典, "Brumer-Stark 予想の証明の概要":

• [DK1]

• Kenneth A. Ribet. “A modular construction of unramified p-extensions of Q(μ_p)”. Invent. Math. 34 (3):151–162, 1976.

• Barry Mazur. “How can we construct abelian Galois extensions of basic number fields?”. Bull. Amer. Math. Soc. (N.S.) 48 (2):155–209, 2011.

• Andrew Wiles. “The Iwasawa conjecture for totally real fields”. Ann. of Math. (2) 131 (3):493–540, 1990.

栗原 将人, "いくつかの Selmer module の導入とその性質":

• [DK1, §§3, 6, A, B]

• Jürgen Ritter and Alfred Weiss. “A Tate sequence for global units”. Compositio Math. 102 (2):147–178, 1996.

• David Burns, Masato Kurihara and Takamichi Sano. “On zeta elements for G_m”. Doc. Math. 21: 555–626, 2016.

• Masato Kurihara, “Notes on the dual of the ideal class groups of CM-fields". J. Théor. Nombr. Bordeaux. 33: 971–996, 2021.

• David Burns, Masato Kurihara and Takamichi Sano, “On Iwasawa theory, zeta elements for G_m, and the equivariant Tamagawa number conjecture.” Algebra and Number Theory. 11: 1527–1571, 2017.

• Masato Kurihara, “Rubin-Stark elements and ideal class groups”. RIMS Kôkyûroku Bessatsu. B53: 343–363, 2015.

熱田 真大, "類数公式による片側の包含への帰着":

• [DK1, §§2, 4, 5, 7.1]

太田 和惟, "Mazur-Tate 予想について":

• Barry Mazur and John Tate. “Refined conjectures of the "Birch and Swinnerton-Dyer type"”. Duke Math. J. 54 (2): 711–750, 1987.

原 隆, "Eisenstein 合同式の手法とその発展について":

• [DK1, §§7, 8], [Sil]

• Kenneth A. Ribet. “A modular construction of unramified p-extensions of Q(μ_p)”. Invent. Math. 34 (3):151–162, 1976.

• Andrew Wiles. “The Iwasawa conjecture for totally real fields”. Ann. of Math. (2) 131 (3):493–540, 1990.

• Joël Bellaïche and Gaësten Chenevier. “Families of Galois representations and Selmer groups”. Astérisque No. 324, xii+314p.p., 2009.

• Samit Dasgupta, Henri Darmon and Robert Pollack. “Hilbert modular forms and the Gross-Stark conjecture”. Ann. of Math. (2) 174 (1):439–484, 2011.

• Christopher Skinner and Eric Urban. “The Iwasawa main conjectures for GL_2”. Invent. Math. 195 (1):1–277, 2014.

• Ming-Lun Hsieh. “Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields”. J. Amer. Math. Soc. 27 (3):753–862, 2014.

並川 健一, "Eisenstein 級数の明示的構成とその定数項":

• [DK1, §§7.3, 8.1], [DK2], [Sil, §§4, 5]

• Goro Shimura. “The special values of the zeta functions associated with Hilbert modular forms”. Duke Math. J. 45 (3):637–679, 1978.

大下 達也, "幾何的ヒルベルト保型形式とダイアモンド作用素":

• [Sil, §§5–7]

佐久川 憲児, "Constant term map の全射性について":

• [Sil, §§8–10]

• Michael Rapoport. “Compactifications de l'espace de modules de Hilbert-Blumenthal”. Compositio Math. 36 (3):255–335, 1978.

• Ching-Li Chai. “Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces”. Ann. of Math. (2) 131 (3):541–554, 1990.

原 隆, "Eisenstein 合同式に現れる尖点形式の構成とヘッケ環の作用について":

• [DK1, §§8.2-8.5], [DK2], [Sil]

吉川 祥, "肥田と Wiles による Galois 表現の構成":

• [DK1, §§9.1, 9.2]

• Andrew Wiles. “On ordinary λ-adic representations associated to modular forms”. Invent. Math. 94 (3):529–573, 1988.

熱田 真大, "Dasgupta-Kakde による主定理の証明の完成":

• [DK1, §§9.3-9.5]

佐野 昂迪: "Hilbert の第12問題への応用: 概要" "Hilbert の第12問題への応用: 整 Gross-Stark 予想の証明":

• [DK3, §§1-4]

加塩 朋和, "CM 周期, 多重ガンマ関数, Stark 予想の関係とその p 進類似":

• Hiroyuki Yoshida. “Absolute CM-periods”. Mathematical Surveys and Monographs, 106. American Mathematical Society, Providence, RI, 2003, x+282 p.p.

• Hiroyuki Yoshida and Tomokazu Kashio. “On p-adic absolute CM-periods. I”. Amer. J. Math. 130 (6):1629–1685, 2008.

• Hiroyuki Yoshida and Tomokazu Kashio. “On p-adic absolute CM-periods. II”. Publ. Res. Inst. Math. Sci. 45 (1):187–225, 2009.

坂本 龍太郎, "Hilbert’s 12th Problem: the vanishing of the Fitting ideal of the Ritter-Weiss module":

• [DK3, §§5, 6]

木村 巌, "Hilbert 第 12 問題の計算例紹介":

• [DK3, §2.3]

• Samit Dasgupta. “Computations of elliptic units for real quadratic fields”. Canad. J. Math. 59 (3):553–574, 2007.

• Max Fleischer and Yijia Liu. “Computations of Brumer-Stark units”. undergraduate research at Duke University.

野村 次郎, "同変岩澤主予想の証明とその応用":

• Henri Johnston and Andreas Nickel. “An unconditional proof of the abelian equivariant Iwasawa main conjecture and applications”, preprint.

• Andreas Nickel. “The strong Stark conjecture for totally odd characters”, preprint.

• Jürgen Ritter and Alfred Weiss. “On the "main conjecture" of equivariant Iwasawa theory”. J. Amer. Math. Soc. 24 (4):1015–1050, 2011.

• Mahesh Kakde. “The main conjecture of Iwasawa theory for totally real fields”. Invent. Math. 193 (3):539–626, 2013.

片岡 武典, "G_m の同変玉河数予想のマイナス成分について":

• Mahiro Atsuta and Takenori Kataoka, “On the minus component of the equivariant Tamagawa number conjecture for G_m”, preprint.