We analyze the notions of indiscernibility and indeterminacy in the light of the Galois theory of field extensions and the generalization to K -algebras proposed by Grothendieck. Grothendieck’s reformulation of Galois theory permits to recast the Galois correspondence between symmetry groups and invariants as a Galois– Grothendieck duality between G-spaces and the minimal observable algebras th...

Let there be given, on a category C, a pair (*, *) of adjoint monoidal closed-category-valued pseudofunctors. Thus, to each object X ∈ C is associated a closed category DX , with unit object OX ; and to each C-map ψ : X → Y , adjoint monoidal functors DX ψ∗ ←−− −→ ψ∗ DY . There are also, as before, compatibilities—expressed by commutative diagrams—among adjunction, pseudofunctoriality, and mono...

In this paper we present a new approach to Grothendieck duality over commutative rings. Our approach is based on the idea of rigid dualizing complexes, which was introduced by Van den Bergh in the context of noncommutative algebraic geometry. The method of rigidity was modified to work over general commutative base rings in our paper [YZ5]. In the present paper we obtain many of the important l...