Derivations and gt-henselian field topologies
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908732359704576 |
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| author | Walsberg, Erik |
| author_facet | Walsberg, Erik |
| contents | Suppose that $K$ is a characteristic zero field with infinite transcendence degree over its prime subfield. We show that if there is a gt-henselian topology on $K$ then there are $2^{2^{|K|}}$ pairwise incomparable gt-henselian topologies on $K$. It follows by applying a recent theorem of Will Johnson that if $K$ is large and countable then there are $2^{2^{\aleph_0}}$ pairwise incomparable gt-henselian topologies on $K$. We also formulate several conjectures concerning gt-henselian field topologies and their relationship with the étale-open topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02889 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derivations and gt-henselian field topologies Walsberg, Erik Logic Commutative Algebra Suppose that $K$ is a characteristic zero field with infinite transcendence degree over its prime subfield. We show that if there is a gt-henselian topology on $K$ then there are $2^{2^{|K|}}$ pairwise incomparable gt-henselian topologies on $K$. It follows by applying a recent theorem of Will Johnson that if $K$ is large and countable then there are $2^{2^{\aleph_0}}$ pairwise incomparable gt-henselian topologies on $K$. We also formulate several conjectures concerning gt-henselian field topologies and their relationship with the étale-open topology. |
| title | Derivations and gt-henselian field topologies |
| topic | Logic Commutative Algebra |
| url | https://arxiv.org/abs/2509.02889 |