In a letter to Quillen from 1985, Deligne proposed a conjectural program suggesting that the degree-one part of the Grothendieck-Riemann-Roch theorem should admit a functorial lift as an isomorphism between two canonically built line bundles. On the one hand, one would have the determinant of the cohomology of Knudsen-Mumford. On the other hand, one would have a refined intersection theoretic construction valued in line bundles. Deligne’s objective was understanding the work of Bismut and coworkers on analytic torsion, and the ongoing developments of Arakelov theory, notably by Gillet and Soulé. Deligne tackled the case of families of curves, and gave a strategy for the intersection theoretic construction valued in line bundles. This gave rise to the so-called Deligne pairings, further developed by Elkik. In the recent years, together with Dennis Eriksson, we have completed Elkik’s work into a genuine relative intersection theory valued in line bundles, and we have accomplished Deligne’s program. In this talk, I will motivate the interest of the problem, by relating it to a mirror symmetry conjecture presented in this seminar in the past, and then explaining our approach and other applications.