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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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
17 November 2023
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| In: |
Forum of mathematics. Sigma
Year: 2023, Volume: 11, Pages: 1-83 |
| ISSN: | 2050-5094 |
| DOI: | 10.1017/fms.2023.82 |
| Online Access: | 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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| Author Notes: | Gebhard Böckle and Ann-Kristin Juschka |
| Summary: | 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 prove the following: The ring 𝑅ps 𝐷 is equidimensional of dimension 𝑑𝑛2 + 1. Its reduced quotient 𝑅univ 𝐷,red contains a dense open subset of regular points x whose associated pseudocharacter 𝐷 𝑥 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 𝑅univ 𝐷 . Similar results were proved by Chenevier for the generic fiber of the universal pseudodeformation ring 𝑅univ 𝐷 of 𝐷. |
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| Item Description: | Gesehen am 10.01.2024 |
| Physical Description: | Online Resource |
| ISSN: | 2050-5094 |
| DOI: | 10.1017/fms.2023.82 |