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http://hdl.handle.net/2445/194821
Title: | A quaternionic construction of p-adic singular moduli |
Author: | Guitart Morales, Xavier Masdeu, Marc Xarles Ribas, Francesc Xavier |
Keywords: | Teoria algebraica de nombres Teoria de cossos de classe Algebraic number theory Class field theory |
Issue Date: | 28-Jun-2021 |
Publisher: | Springer Nature Switzerland |
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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s40687-021-00274-3 |
It is part of: | Research in the Mathematical Sciences, 2021, vol. 8 |
URI: | http://hdl.handle.net/2445/194821 |
Related resource: | https://doi.org/10.1007/s40687-021-00274-3 |
ISSN: | 2522-0144 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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