Our project lies at the intersection of number theory, representation theory and commutative algebra. More precisely, given an odd prime integer p, it aims at studying the feasibility of a p-modular version of Langlands and Shimura correspondences for p-adic metaplectic groups, i.e. to study what happens when one replaces the field of complex numbers C by an algebraic closure Fp of the field with p elements in this two frameworks.