Peiduo Wang

In this talk, 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 Gachets 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.