2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149157This paper is the first in a series. The main goal of the series is to present a geometric construction of certain remarkable tensor categories arising from quantum groups coresponding to the value of deformation parameter $q$ equal to a root of unity. In the present paper we study perverse sheaves over a complex affine space which are smooth along the stratification determined by a finite arrangement of complex affine hyperplanes defined by real equations. In particular, we construct explicitely (in terms of combinatorial data) complexes computing cohomology of Goresky-MacPherson extensions of one-dimensional local systems over the complement of hyperplanes.26 pages, amslatex. A misprint correctedHigh Energy Physics - TheoryAlgebraic GeometryQuantum Algebratext