Stable equivalence of 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...

Derived Equivalence and Stable Equivalence of Repetitions

For repetitions (= repetitive \algebras") of algebras of nite global dimension we will show that there exists a triangle equivalence between their bounded derived categories of nitely presented modules ii there exists a triangle equivalence between their stable categories of nitely presented modules.

Stable Reductive Varieties I: Affine Varieties

0. Introduction 1 1. Main definitions and results 3 2. General criteria 6 2.1. Seminormality and connectedness of isotropy groups 6 2.2. Finiteness of number of orbits and group–like condition 9 3. Orbits in stable reductive varieties 11 3.1. Isotropy groups 11 3.2. Algebras of regular functions 14 4. Reductive varieties 18 4.1. Classification 18 4.2. Associated stable toric varieties 20 5. Sta...

Dualizing Complexes

Stable Equivalence of Differentiable Manifolds

A natural question, of great generality, various special forms of which are often asked in differential topology, is the following: Let Mi, Mi be differentiable w-manifolds, : M\—»M2 a continuous map which is a homotopy equivalence between M\ and M2. When is there a differentiable isomorphism <3>: Mi—> M2 in the same homotopy class as 0? For example, there is the Poincaré Conjecture which po...