Takumi Watanabe

collaborators

2 papers

math.NT2026

On the $(I ¨ , I^)$ -modules corresponding to crystalline representations

Takumi Watanabe

Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p > 0$ . We introduce the notion of crystalline $(I ¨ , I^)$ -modules ov…

math.NT2026

A remark on an integral structure of the imperfect coefficient ring of $(I ¨ , I^)$ -modules

Takumi Watanabe

Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p > 0$ . Let $A_{K}$ denote the imperfect coefficient ring of…

On the (I¨,I^)-modules corresponding to crystalline representations

A remark on an integral structure of the imperfect coefficient ring of (I¨,I^)-modules

On the $(I ¨ , I^)$ -modules corresponding to crystalline representations

A remark on an integral structure of the imperfect coefficient ring of $(I ¨ , I^)$ -modules