On The Adic Formalism
This article is concerned with developing a formalism for complexes of ℓ-adic sheaves instead of just for the sheaves themselves as was done in [SGA5:Exp.V]. The need for such a generalisation has become apparent from the theory of perverse sheaves, which by their definition are complexes of ℓ-adic sheaves. When trying to carry through such an extension one is immediately faced with two problems. On the one hand it is clear already from the case of ℓ-adic sheaves that — contrary to the case of torsion sheaves — one is not dealing with actual sheaves but rather inverse systems of sheaves. On the other hand one wants to pretend that one is dealing with sheaves and not some more abstract objects.
KeywordsFinite Type Mapping Cone Triangulate Category Inverse System Natural Morphism
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