an:01414388
Zbl 0945.14013
Grosse-Kl??nne, Elmar
Rigid analytic spaces with overconvergent structure sheaf
EN
J. Reine Angew. Math. 519, 73-95 (2000).
00063083
2000
j
14G22 32P05 32C36
rigid space; dagger space; Serre duality; overconvergent structure; de Rham cohomology; Poincar?? duality
It is known that the de Rham cohomology of a smooth rigid space \(X\), which admits a closed immersion into a polydisk without boundary is (generically) finite dimensional, and there is a Serre duality for \(X\). These fail for an affinoid smooth rigid space, which admits a closed immersion into a polydisk with boundary.
The author introduces a category of rigid spaces with an overconvergent structure sheaf, which improves this situation. Versions of the Serre and Poincar?? duality are proved. An interpretation in terms of the new category is given for the rigid cohomology introduced recently by P. Berthelot.
Anatoly N.Kochubei (Kiev)