Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/194821
A quaternionic construction of p-adic singular moduli
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
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.
Matèries (anglès)
Citació
Citació
GUITART MORALES, Xavier, MASDEU, Marc, XARLES RIBAS, Francesc xavier. A quaternionic construction of p-adic singular moduli. _Research in the Mathematical Sciences_. 2021. Vol. 8. [consulta: 24 de gener de 2026]. ISSN: 2522-0144. [Disponible a: https://hdl.handle.net/2445/194821]