松江数論セミナー
松江数論セミナー
セミナー予定
第6回 2025年12月18日(木)
場所：島根大学松江キャンパス 総合理工学部3号館 6階 数理第２総合演習室
10:00-11:30 講演者：Kalyan Chakraborty（SRM University, Andhra Pradesh)
題目： From algebraic curves to class groups of number fields
概要： The talk will be in two parts:
1st Part: In this talk, I will briefly recall a technique of Soleng to produce high order elements of class groups of quadratic fields starting from an elliptic curve over \({\mathbb Q}\) with a non-trivial torsion. I will present a generalization of this technique to the family of class groups of quadratic fields starting from an elliptic surface defined over \({\mathbb Q}\). This is a joint work with Banerjee and Hoque (appeared in Research in Number Theory).
2nd Part: In this talk we recall work of Banerjee-Hoque relating l-torsion in the Picard group of certain hyperelliptic curves to the l-torsion of certain imaginary quadratic fields. Then I will present two families of imaginary biquadratic fields with large class groups. This is joint with Banerjee and Ghosh (appeared in Research in Number Theory).
13:30-15:00 講演者：水野 義紀 (名古屋工業大学)
題目： A generalization of Girstmair's formula
概要： In 1994, K. Girstmair discovered a surprising connection between digits of the base \(g\) expansion of \(1/p\)
and the class number \(h(-p)\) of \({\mathbb Q}(\sqrt{-p})\), where \(p\) is a prime with \(p\equiv 3\) (mod 4). We discuss a generalization of Girstmair's formula. In particular, Girstmair's formula is generalized to the case \(p\equiv 1\) (mod 4).
15:20-16:50 講演者：藤井 俊 (島根大学)
題目： On pseudo-null submodules of unramified Iwasawa modules of \({\Bbb Z}_p^d\)-extensions
概要： Let \(p\) be a prime number and \(k/{\Bbb Q}\) a finite extension.
It is conjectured by Greenberg that the unramified
Iwasawa module \(X\) of the maximal multiple \({\Bbb Z}_p\)-extension
of \(k\) is always pseudo-null for all \(k\).
It is not known whether \(X\) contains a non-trivial pseudo-null submodule or not when \(X\) is not trivial.
In this talk, we will discuss conditions under which \(X\) has a
non-triviall pseudo-null submodule.
16:50- 自由討論
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世話人
青木 美穂
aoki(at)riko.shimane-u.ac.jp
藤井 俊
fujiisatoshi(at)edu.shimane-u.ac.jp
山本 修司
yamashu(at)riko.shimane-u.ac.jp