Elementary anabelian varieties are anabelian
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910172396388352 |
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| author | Carlson, Magnus |
| author_facet | Carlson, Magnus |
| contents | We show that isomorphisms of fundamental groups of elementary anabelian varieties -- varieties obtained as iterated fibrations of hyperbolic curves -- over sub-$p$-adic fields correspond bijectively to isomorphisms of varieties. Moreover, dominant maps between proper elementary anabelian varieties are in bijection with ``stably cohomologically injective'' maps of fundamental groups: open maps whose pullbacks to all open subgroups induce injections on cohomology rings with $\ell$-adic coefficients, for any prime $\ell$. This verifies conjectures of Grothendieck from his letter to Faltings. Finally, we establish étale homotopical generalizations of these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24898 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Elementary anabelian varieties are anabelian Carlson, Magnus Number Theory Algebraic Geometry 14F35 We show that isomorphisms of fundamental groups of elementary anabelian varieties -- varieties obtained as iterated fibrations of hyperbolic curves -- over sub-$p$-adic fields correspond bijectively to isomorphisms of varieties. Moreover, dominant maps between proper elementary anabelian varieties are in bijection with ``stably cohomologically injective'' maps of fundamental groups: open maps whose pullbacks to all open subgroups induce injections on cohomology rings with $\ell$-adic coefficients, for any prime $\ell$. This verifies conjectures of Grothendieck from his letter to Faltings. Finally, we establish étale homotopical generalizations of these results. |
| title | Elementary anabelian varieties are anabelian |
| topic | Number Theory Algebraic Geometry 14F35 |
| url | https://arxiv.org/abs/2604.24898 |