ar X iv : a lg - g eo m / 9 70 80 06 v 2 1 4 O ct 1 99 8 DUALITY AND FLAT BASE CHANGE ON FORMAL SCHEMES
نویسنده
چکیده
We give several related versions of global Grothendieck Duality for unbounded complexes on noetherian formal schemes. The proofs, based on a nontrivial adaptation of Deligne’s method for the special case of ordinary schemes, are reasonably self-contained, modulo the Special Adjoint Functor Theorem. An alternative approach, inspired by Neeman and based on recent results about “Brown Representability,” is indicated as well. A section on applications and examples illustrates how our results synthesize a number of different duality-related topics (local duality, formal duality, residue theorems, dualizing complexes, . . . ). A flat-base-change theorem for pseudo-proper maps leads in particular to sheafified versions of duality for bounded-below complexes with quasi-coherent homology. Thanks to Greenlees-May duality, the results take a specially nice form for proper maps and bounded-below complexes with coherent homology.
منابع مشابه
ar X iv : h ep - t h / 05 06 18 8 v 2 1 9 Ju l 2 00 5 Classical solution of a sigma model in curved background
We have solved equations of motion of a σ–model in curved background using the fact that the Poisson–Lie T-duality can transform them into the equations in the flat one. For finding solution of the flat model we have used transformation of coordinates that makes the metric constant. The T-duality transform was then explicitly performed.
متن کاملar X iv : d g - ga / 9 40 70 08 v 1 2 0 Ju l 1 99 4 JUMPS OF THE ETA - INVARIANT
In [2], Atiyah, Patodi and Singer introduced an invariant ηD of any self-adjoint elliptic differential operator D on an odd-dimensional oriented closed manifold M , in order to prove an index theorem for manifolds with boundary. For the germinal case of the “signature operator”the relevant D is ±(∗d− d∗), where the Hodge duality operator ∗ is determined by the Reimannian metric on M . They cons...
متن کاملar X iv : h ep - t h / 95 04 01 9 v 2 1 7 M ay 1 99 5 DAMTP / R - 95 / 8 Duality between Electric and Magnetic Black Holes
A number of attempts have recently been made to extend the conjectured S duality of Yang Mills theory to gravity. Central to these speculations has been the belief that electrically and magnetically charged black holes, the solitons of quantum gravity, have identical quantum properties. This is not obvious, because although duality is a symmetry of the classical equations of motion, it changes ...
متن کاملar X iv : h ep - t h / 93 09 06 7 v 1 1 0 Se p 19 93 Strings , Loops , Knots and Gauge Fields
The loop representation of quantum gravity has many formal resemblances to a background-free string theory. In fact, its origins lie in attempts to treat the string theory of hadrons as an approximation to QCD, in which the strings represent flux tubes of the gauge field. A heuristic path-integral approach indicates a duality between background-free string theories and generally covariant gauge...
متن کاملT-duality, Non-geometry and Lie Algebroids in Heterotic Double Field Theory
A number of issues in heterotic double field theory are studied. This includes the analysis of the T-dual configurations of a flat constant gauge flux background, which turn out to be non-geometric. Performing a field redefinition to a nongeometric frame, these T-duals take a very simple form reminiscent of the constant Qand R-flux backgrounds. In addition, it is shown how the analysis of arXiv...
متن کامل