Tohoku Mathematical Journal
2024
December
SECOND SERIES VOL. 76, NO. 4

Tohoku Math. J.
76 (2024), 483-520

Title ON GENERALIZED FUCHS THEOREM OVER $p$-ADIC POLYANNULI

Author Peiduo Wang

(Received July 5, 2022, revised February 24, 2023)
Abstract. In this paper, we study finite projective differential modules on $p$-adic polyannuli satisfying the Robba condition. Christol and Mebkhout proved the decomposition theorem (the $p$-adic Fuchs theorem) of such differential modules on one dimensional $p$-adic annuli under certain non-Liouvilleness assumption and Gachet generalized it to higher dimensional cases. On the other hand, Kedlaya proved a generalization of the $p$-adic Fuchs theorem in one dimensional case. We prove Kedlaya's generalized version of $p$-adic Fuchs theorem in higher dimensional cases.

Mathematics Subject Classification. Primary 12H25; Secondary 14G22.
Key words and phrases. $p$-adic differential equations, $p$-adic Fuchs theorem, polyannuli.

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