An analytic approach to $P$-adic diffeomorphism group and Teichmüller theory
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911535076474880 |
|---|---|
| author | Lu, Yuxiu |
| author_facet | Lu, Yuxiu |
| contents | We consider a specific class of infinite dimensional $p$-adic Lie groups, i.e., a sort of diffeomorphism groups on $p$-adic ball $\operatorname{Diff}^{\operatorname{an}}(B_ε)$. It turns out that this group has a natural logarithmic structure that leads to a $p$-adic version of Teichmüller theory on diffeomorphism groups, which also presents some remarkable hydrodynamic facets. We further apply this framework to Mochizuki's $p$-adic Teichmüller theory and Inter-universal Teichmüller theory (IUT), and give a new reformulation of IUT as a Teichmüller theory on automorphisms of two-dimensional group schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21074 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An analytic approach to $P$-adic diffeomorphism group and Teichmüller theory Lu, Yuxiu Number Theory Algebraic Geometry We consider a specific class of infinite dimensional $p$-adic Lie groups, i.e., a sort of diffeomorphism groups on $p$-adic ball $\operatorname{Diff}^{\operatorname{an}}(B_ε)$. It turns out that this group has a natural logarithmic structure that leads to a $p$-adic version of Teichmüller theory on diffeomorphism groups, which also presents some remarkable hydrodynamic facets. We further apply this framework to Mochizuki's $p$-adic Teichmüller theory and Inter-universal Teichmüller theory (IUT), and give a new reformulation of IUT as a Teichmüller theory on automorphisms of two-dimensional group schemes. |
| title | An analytic approach to $P$-adic diffeomorphism group and Teichmüller theory |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2603.21074 |