We define \emph{ $0$-shifted} and \emph{ $+1$-shifted contact structures} on differentiable stacks, thus laying the foundations of \emph{ shifted Contact Geometry}. As a side result we show that the kernel of a multiplicative $1$-form on a Lie groupoid (might not exist as a Lie groupoid but it) always exists as a differentiable stack, and it is naturally equipped with a stacky version of the curvature of a distribution. Contact structures on orbifolds provide examples of $0$-shifted contact structures, while prequantum bundles over $+1$-shifted symplectic groupoids provide examples of $+1$-shifted contact structures. Our shifted contact structures are related to shifted symplectic structures via a Symplectic-to-Contact Dictionary.
Categories: math.DG math-ph math.MP math.SG