[Note sur la formule de Coleman pour la Frobenius absolue sur les courbes de Fermat]
Coleman a calculé explicitement le Frobenius absolu sur les courbes de Fermat. Dans cet article, nous montrons qu’une sorte de continuité -adique implique une grande partie de sa formule. Pour ce faire, nous étudions une relation entre les équations fonctionnelles de la fonction gamma, les relations monomiales sur CM-périodes, et leurs analogues -adiques.
Coleman calculated the absolute Frobenius on Fermat curves explicitly. In this paper we show that a kind of -adic continuity implies a large part of his formula. To do this, we study a relation between functional equations of the gamma function, monomial relations on CM-periods, and their -adic analogues.
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Keywords: Absolute Frobenius, Fermat curves, Gross–Koblitz formula, $p$-adic gamma function, CM-periods, $p$-adic periods.
Mot clés : Frobenius absolu, courbes de Fermat, formule de Gross–Koblitz, fonction gamma $p$-adique, CM-périodes, périodes $p$-adiques.
@unpublished{AIF_0__0_0_A62_0,
author = {Kashio, Tomokazu},
title = {Note on {Coleman{\textquoteright}s} formula for the absolute {Frobenius} on {Fermat} curves},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
year = {2024},
doi = {10.5802/aif.3615},
language = {en},
note = {Online first},
}
Kashio, Tomokazu. Note on Coleman’s formula for the absolute Frobenius on Fermat curves. Annales de l'Institut Fourier, Online first, 22 p.
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