This paper is the revised version of paragraphs 6 and 7 of Polylogarithmic Extensions on Mixed Shimura varieties. Its subject is the generalization of the construction of polylogarithmic extensions to the context of mixed Shimura varieties. After the definition of Pol, we discuss its main features: rigidity, norm compatibility, and values at Levi sections. We also generalize Beilinson's and Levin's definition of the small polylogarithm pol. Our results depend on those contained in "The canonical construction of mixed sheaves on mixed Shimura varieties", which will soon be added to the archive.
This paper is now available in Springer Lecture Notes in Mathematics, number 1650.