I will introduce the rational analytic syntomification of a partially proper rigid space over Q_p, which is a stack geometrising syntomic cohomology in the sense of Colmez--Niziol. This leads to a notion of syntomic cohomology of rigid spaces with coefficients and I will discuss
(1) what this category of coefficients is in more classical terms and
(2) how to use the geometry of the syntomification to prove p-adic comparison theorems for rigid-analytic varieties with coefficients.
Time permitting, I will also sketch an extension of these ideas to integral coefficients.
