Modular sheaves of de Rham classes on Hilbert formal modular schemes for unramified primes

We define formal vector bundles with marked sections on Hilbert modular schemes and we show how to use them to construct modular sheaves with an integrable meromorphic connection and a filtration which, in degree 0, gives to us a $p$-adic interpolation of the usual Hodge filtration. We relate it with the sheaf of overconvergent Hilbert modular forms.