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DC Field | Value | Language |
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dc.contributor.author | Guitart Morales, Xavier | - |
dc.contributor.author | Masdeu, Marc | - |
dc.contributor.author | Xarles Ribas, Francesc Xavier | - |
dc.date.accessioned | 2023-03-08T07:43:40Z | - |
dc.date.available | 2023-03-08T07:43:40Z | - |
dc.date.issued | 2021-06-28 | - |
dc.identifier.issn | 2522-0144 | - |
dc.identifier.uri | http://hdl.handle.net/2445/194821 | - |
dc.description.abstract | Rigid meromorphic cocycles were introduced by Darmon and Vonk as a conjectural $p$-adic extension of the theory of singular moduli to real quadratic base fields. They are certain cohomology classes of $\mathrm{SL}_2(\mathbb{Z}[1 / p])$ which can be evaluated at real quadratic irrationalities, and the values thus obtained are conjectured to lie in algebraic extensions of the base field. In this article, we present a construction of cohomology classes inspired by that of DarmonVonk, in which $\mathrm{SL}_2(\mathbb{Z}[1 / p])$ is replaced by an order in an indefinite quaternion algebra over a totally real number field $F$. These quaternionic cohomology classes can be evaluated at elements in almost totally complex extensions $K$ of $F$, and we conjecture that the corresponding values lie in algebraic extensions of $K$. We also report on extensive numerical evidence for this algebraicity conjecture. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Springer Nature Switzerland | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1007/s40687-021-00274-3 | - |
dc.relation.ispartof | Research in the Mathematical Sciences, 2021, vol. 8 | - |
dc.relation.uri | https://doi.org/10.1007/s40687-021-00274-3 | - |
dc.rights | (c) Springer Nature Switzerland, 2021 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Teoria algebraica de nombres | - |
dc.subject.classification | Teoria de cossos de classe | - |
dc.subject.other | Algebraic number theory | - |
dc.subject.other | Class field theory | - |
dc.title | A quaternionic construction of p-adic singular moduli | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 720805 | - |
dc.date.updated | 2023-03-08T07:43:40Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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720805.pdf | 386.19 kB | Adobe PDF | View/Open |
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