Equidimensionality of universal pseudodeformation rings in characteristic p for absolute Galois groups of p-adic fields
Let K be a finite extension of the p-adic field Q𝑝 of degree d, let F be a finite field of characteristic p and let 𝐷 be an n-dimensional pseudocharacter in the sense of Chenevier of the absolute Galois group of K over the field F. For the universal mod p pseudodeformation ring 𝑅univ 𝐷 of 𝐷, we prov...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
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17 November 2023
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| In: |
Forum of mathematics. Sigma
Year: 2023, Jahrgang: 11, Pages: 1-83 |
| ISSN: | 2050-5094 |
| DOI: | 10.1017/fms.2023.82 |
| Online-Zugang: | Verlag, kostenfrei, Volltext: https://doi.org/10.1017/fms.2023.82 Verlag, kostenfrei, Volltext: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/equidimensionality-of-universal-pseudodeformation-rings-in-characteristic-p-for-absolute-galois-groups-of-padic-fields/E29626E5A2A247CD54CB5C98F6AB21A5 
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| Verfasserangaben: | Gebhard Böckle and Ann-Kristin Juschka |
MARC
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| 520 | |a Let K be a finite extension of the p-adic field Q of degree d, let F be a finite field of characteristic p and let be an n-dimensional pseudocharacter in the sense of Chenevier of the absolute Galois group of K over the field F. For the universal mod p pseudodeformation ring univ of , we prove the following: The ring ps is equidimensional of dimension 2 + 1. Its reduced quotient univ ,red contains a dense open subset of regular points x whose associated pseudocharacter is absolutely irreducible and nonspecial in a certain technical sense that we shall define. Moreover, we will characterize in most cases when K does not contain a p-th root of unity the singular locus of Spec univ . Similar results were proved by Chenevier for the generic fiber of the universal pseudodeformation ring univ of . | ||
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