This work establishes the geometric component of Deligne's longstanding program on refined Grothendieck-Riemann-Roch formulas expressed through determinants of cohomology. The approach relies on a newly developed universal category of Chern classes together with an associated relative intersection theory. As an example of the applications, we provide a structural description of the coefficients in the Knudsen-Mumford expansion and establish a fundamental Mumford-type isomorphism for the alternating product of Griffiths bundles.
Categories: math.AG