Residues And Duality

  title={Residues And Duality},
  author={Robin Hartshorne},

The Nakayama functor and its completion for Gorenstein algebras.

Duality properties are studied for a Gorenstein algebra that is finite and projective over its center. Using the homotopy category of injective modules, it is proved that there is a local duality

Smooth representations and Hecke modules in characteristic p

Let G be a p-adic Lie group and I ⊆ G be a compact open subgroup which is a torsionfree pro-p-group. Working over a coefficient field k of characteristic p we introduce a differential graded Hecke

On the infinitesimal theory of Chow groups

The Chow groups of codimension-p algebraic cycles modulo rational equivalence on a smooth algebraic variety X have steadfastly resisted the efforts of algebraic geometers to fathom their structure.

Contracting endomorphisms and dualizing complexes

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring R. Our focus is on homological properties of contracting endomorphisms of R,

Explicit calculation of Frobenius isomorphisms and Poincar\'{e} duality in the theory of arithmetic $\mathscr{D}$-modules

The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic $\ms{D}$-modules. To do this, we calculate explicitly an isomorphism between canonical

Reflexivity and rigidity for complexes, II: Schemes

We prove basic facts about reflexivity in derived categories over noetherian schemes; and about related notions such as semidualizing complexes, invertible complexes, and Gorenstein-perfect maps.

Rigid Dualizing Complexes via Differential Graded Algebras (Survey)

In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their

Variance And Duality For Cousin Complexes On Formal Schemes

Part 1. Pseudofunctorial behavior of Cousin complexes on formal schemes by J. Lipman, S. Nayak, and P. Sastry Part 2. Duality for Cousin complexes by P. Sastry Part 3. Pasting pseudofunctors by S.

Reflexivity and Ring Homomorphisms of Finite Flat Dimension

In this article we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings. One primary