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- W3076200412 abstract "Arithmetic differential equations or δ-geometry exploits analogies between derivations and p-derivations δ arising from lifts of Frobenius to study problems in arithmetic geometry. Along the way, two main classes such functions, describable as series, arose prominently namely δ-characters of abelian schemes and (isogeny covariant) δ-modular forms. However, the theory of these δ-functions is not as straightforward in ramified settings. Overconvergence was introduced in [13] to account for these issues which essentially imposes growth conditions extensions of these series to a fixed level of ramification; necessary as such extensions have non-trivial fractional coefficients. In this article, we introduce a rescaling process which identifies a class of δ-functions we call totally overconvergent, which extend all the way to the algebraic closure of ring of integers of the maximally unramified extension of Qp. Applications built on these functions allow one to remove boundedness assumptions on ramification. The bulk of the article is devoted to establishing that most δ-functions arising in practice, namely those in the applications described in [5], [7], [8], are totally overconvergent, which essentially extends results in [13] to unbounded ramification." @default.
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- W3076200412 date "2020-12-01" @default.
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- W3076200412 title "Solutions to arithmetic differential equations in algebraically closed fields" @default.
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- W3076200412 doi "https://doi.org/10.1016/j.aim.2020.107342" @default.
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