PreprintCC BY 4.0HAL
Théories relatives pour les équations différentielles p-adiques : Le cas des modules de Robba
Abstract
The "monodromy theorem" for p-adic differential equations says that a "Robba module of which exponent has non Liouville differences" is "regular", namely has a basis in which the matrix of the derivation x d /dx is constant. In this paper the monodromy theorem is proved replacing the (p-adic) field of constants by a p-adic algebra of constants. In other words, instead of one single p-adic differential equation it looks at a family of p-adic differential equations parametrized by the maximal ideals of B. Both cases when B is an affinoïd algebra and when B is a dagger algebra are examined. The second one is much more tricky but more valuable for characteristic p algebraic geometry applications.
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BibTeX
@misc{christol2026théories,
title = {{Théories relatives pour les équations différentielles p-adiques : Le cas des modules de Robba}},
author = {G Christol},
howpublished = {HAL},
year = {2026},
month = jun,
url = {https://hal.science/hal-05657933v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Théories relatives pour les équations différentielles p-adiques : Le cas des modules de Robba
AU - G Christol
PY - 2026
DA - 2026/06/15
PB - HAL
UR - https://hal.science/hal-05657933v2
AB - The "monodromy theorem" for p-adic differential equations says that a "Robba module of which exponent has non Liouville differences" is "regular", namely has a basis in which the matrix of the derivation x d /dx is constant. In this paper the monodromy theorem is proved replacing the (p-adic) field of constants by a p-adic algebra of constants. In other words, instead of one single p-adic differential equation it looks at a family of p-adic differential equations parametrized by the maximal ideals of B. Both cases when B is an affinoïd algebra and when B is a dagger algebra are examined. The second one is much more tricky but more valuable for characteristic p algebraic geometry applications.
ER -