Stable equivalence of dualizing R-varieties. II. Hereditary dualizing R-varieties

Rational Points, R-equivalence and Étale Homotopy of Algebraic Varieties

We study a generalisation of the anabelian section conjecture of Grothendieck by substituting the arithmetic fundamental group with a relative version of the étale homotopy type. We show that the map associating homotopy fixed points to rational points factors though R-equivalence for projective varieties defied over fields of characteristic zero. We show that over p-adic fields rational points...

Dualizing Complexes

Recognizing Dualizing Complexes

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extension A ⋉M is a Gorenstein Differential Graded Algebra. As a corollary follows that A has a dualizing complex if and only if it is a quotient of a Gorenstein local Differential Graded Algebra. Let A be a noetherian local ...

On Matlis Dualizing Modules

We consider rings admitting a Matlis dualizing module E. We argue that if R admits two such dualizing modules, then a module is reflexive with respect to one if and only if it is reflexive with respect to the other. Using this fact we argue that the number (whether finite or infinite) of distinct dualizing modules equals the number of distinct invertible (R,R)-bimodules. We show by example that...

Dualizing the Coarse Assembly Map

We formulate and study a new coarse (co-)assembly map. It involves a modification of the Higson corona construction and produces a map dual in an appropriate sense to the standard coarse assembly map. The new assembly map is shown to be an isomorphism in many cases. For the underlying metric space of a group, the coarse co-assembly map is closely related to the existence of a dual Dirac morphis...