月齢報告会とは、主に大学院生を対象とした会で、研究の進捗状況を報告したり、大学院生の研究のネタとなる課題を提供したりすることを目的としています。月に一度程度の間隔で開催しており、2020年9月から継続しています。
開催当初は満月の夜に合わせて実施していたため、毎月月齢を調べていました。その経緯から「月例報告会」ではなく「月齢報告会」と名付けられました。
UPCOMING SEMMINAR
第63回
日時:2026年4月24日(金) 16:30-(日本時間)
開催方法:オンライン開催(zoom)
講演者 : Muller Joseph (NCTS, National Taiwan University)
タイトル: Kraft quivers and twisted Gelfand-Ponomarev modules
アブストラクト: Let $K$ be any field and let $\sigma, \tau$ be two automorphisms of $K$. We consider the $K$-algebra $K[F,V]_{\sigma,\tau}$ generated by two indeterminates $F$ and $V$, which are respectively $\sigma$-linear and $\tau$-linear, and which satisfy $FV = VF = 0$. Finite dimensional left $K[F,V]_{\sigma,\tau}$-modules are called "twisted Gelfand-Ponomarev modules". In this talk, we explain how these can be classified by semilinear representations of Kraft quivers. This is a special case of the classification of modules over semilinear path algebras by "strings" and "bands", which has been first witnessed by the seminal work of Gelfand and Ponomarev (1968) and Ringel (1975), and later formalized by Butler and Ringel (1987). More recent generalizations are due to Crawley-Boevey (2017), and Bennett-Tennenhaus and Crawley-Boevey (2024) in the semi-linear case.
One motivation for classifying modules over $K[F,V]_{\sigma,\tau}$ is the case where $K$ is perfect of positive characteristic, $\sigma$ is the Frobenius morphism and $\tau = \sigma^{-1}$. In this case, $K[F,V]_{\sigma,\tau}$ is the usual Dieudonné ring modulo $p$, and by Dieudonné theory, twisted Gelfand-Ponomarev modules correspond to commutative group schemes over $K$ which are killed by $p$. In 1975, Kraft used this classification to study $p$-torsion subgroups of abelian varieties over $K$. One other application is to give a direct proof of Theorem 6.1 of Kottwitz and Rapoport's paper On the existence
of F-crystals (2003), which was used to prove the converse of Mazur's inequality.
This talk is based on a survey paper which is joint work with Chia-Fu Yu.
代表:
2020/10-2022/12 松月
2022/12-2024/06 安澤
2024/07-2024/08 片山
2024/09-現在 范