On the chromatic number of the space Qn

This work deals with the classical Nelson-Hadwiger problem of the chromatic number of space. We consider a generalization of this problem to the case of the space Qn. We introduce the new quantity χaff(Qn) equal to the maximum value of the chromatic number of a distance graph whose vertices lie in an affine subspace of dimension n in a space Qm and whose edges are generated by a rational distance. We prove new bounds on this quantity.