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Theory of p-adic differential equations (pDEs) is a highly developed subject with a history more than 50 years. It initially appeared in number theory in Dwork’s work and is found to have important connections with other areas in number theory. pDEs satisfying the Robba condition is one kind that we are interested in. These differential modules play a very important role and are also easier to treat. We are also interested in general pDEs and their applications to ramification theory. Our motivation for this topic comes from equivalence of differential and Arithmetic Swan conductors.
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