Residue of special functions of Anderson $A$-modules at the characteristic graph
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866915809903771648 |
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| author | Gazda, Quentin Maurischat, Andreas |
| author_facet | Gazda, Quentin Maurischat, Andreas |
| contents | Let $E$ be an Anderson $A$-module over $\mathbb{C}_{\infty}$. The period lattice of $E$ is related to its module of special functions by means of a non-canonical isomorphism introduced by the authors in [GM21]. In this paper, we explain how a modification of the inverse map is canonical by interpreting it as a residue morphism along the characteristic graph. This phenomenon has already been observed in various situations. The main innovation of this text is that of costability (costable admissible opens, costable site, etc.) which provides a convenient framework to develop the notion of sheaves of $E(\mathbb{C}_{\infty})$-valued meromorphic functions on the rigid analytic plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08121 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Residue of special functions of Anderson $A$-modules at the characteristic graph Gazda, Quentin Maurischat, Andreas Number Theory Algebraic Geometry 11G09 (Primary) 11R58, 11J93, 14H05 (Secondary) Let $E$ be an Anderson $A$-module over $\mathbb{C}_{\infty}$. The period lattice of $E$ is related to its module of special functions by means of a non-canonical isomorphism introduced by the authors in [GM21]. In this paper, we explain how a modification of the inverse map is canonical by interpreting it as a residue morphism along the characteristic graph. This phenomenon has already been observed in various situations. The main innovation of this text is that of costability (costable admissible opens, costable site, etc.) which provides a convenient framework to develop the notion of sheaves of $E(\mathbb{C}_{\infty})$-valued meromorphic functions on the rigid analytic plane. |
| title | Residue of special functions of Anderson $A$-modules at the characteristic graph |
| topic | Number Theory Algebraic Geometry 11G09 (Primary) 11R58, 11J93, 14H05 (Secondary) |
| url | https://arxiv.org/abs/2211.08121 |