Аннотация:The concept of schematization consists in replacing simplicial groups by
simplicial affine group schemes. In the case when the coefficient field has zero characteristic, there is a prominent theory of simplicial prounipotent groups, the origins of which lead to the rational homotopy theory of D. Quillen. It turns out that
schematization reveals the profound properties of Fp–prounipotent groups, especially in connection with prounipotent groups in zero characteristic and in the study
of quasirationality. In this paper, using results on representations and cohomology
of prounipotent groups in characteristic 0, we prove an analogue of Lyndon Identity
theorem for one-relator pro-p-groups (question posed by J.P. Serre) and demonstrate
the application to one more problem of J.-P. Serre concerning one-relator pro–p–
groups of cohomological dimension 2. Schematic approach makes it possible to
consider the problems of pro–p–groups theory through the prism of Tannaka duality, concentrating on the category of representations. In particular we attach special
importance to the existence of identities in free pro–p–groups (“conjurings”).