In this paper we introduce the category of stratified pro-modules and the notion of induced object in this category. We propose a translation of Saito equivalence results (Bull. Soc. Math France 117:361–387, 1989) using the dual language of pro-objects. So we prove an equivalence between the derived category of stratified pro-modules and the category of prodifferential complexes. We also supply a comparison with the notion of crystal in pro-module (introduced by P. Deligne in 1970).
Differential complexes and stratified pro-modules
FIOROT, LUISA
2011
Abstract
In this paper we introduce the category of stratified pro-modules and the notion of induced object in this category. We propose a translation of Saito equivalence results (Bull. Soc. Math France 117:361–387, 1989) using the dual language of pro-objects. So we prove an equivalence between the derived category of stratified pro-modules and the category of prodifferential complexes. We also supply a comparison with the notion of crystal in pro-module (introduced by P. Deligne in 1970).
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