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When is the étale open topology a field topology?

Abstract:

We investigate the following question: Given a field K, when is the ´etale open topology EK induced by a field topology? On the positive side, when K is the fraction field of a local domain R 6= K, using a weak form of resolution of singularities due to Gabber, we show that EK agrees with the R-adic topology when R is quasi-excellent and henselian. Various pathologies appear when dropping the quasi-excellence assumption. For locally bounded field topologies, we introduce the notion of general...

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Publication status:
Accepted
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Springer
Journal:
Israel Journal of Mathematics More from this journal
Acceptance date:
2023-02-21
EISSN:
1565-8511
ISSN:
0021-2172
Language:
English
Keywords:
Pubs id:
1338178
Local pid:
pubs:1338178
Deposit date:
2023-04-21

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