Residues and differential operators on schemes Academic Article uri icon


  • 0. Introduction 305 1. Review of Beilinson completion algebras 307 2. Construction of the residue complex;: Jc 310 3. Duality for proper morphisms 316 4. Duals of differential operators 319 5. The de Rham residue complex 323 6. de Rham homology and theniveau spectral sequence 325 7. The intersection cohomology-module of a curve 332 0. Introduction. Suppose X is a finite-type scheme over a field k, with struc-tural morphism rr. Consider the twisted inverse image functor re!" Dc+(k) Dc+(X) of Grothendieck duality theory (see [Hall). The residue complex:'Jc is defined to be the Cousin complex of zr! k. It is a bounded complex of quasi-coherent 60x-modules, possessing remarkable functorial properties. In this paper we provide an explicit construction of Jc. This construction reveals some new properties of o: jc and also has applications in other areas of algebraic …

publication date

  • January 1, 1998