Abstract
The importance of this point of view is apparent, since it suggests one possible way of extending (abelian) class field theory to more general schemes. For instance, Artin-Verdier duality holds also for X a smooth proper curve over a finite field [S], again with G, as the dualizing sheaf. However, G, is not able to play this role in more general situations, when we allow singularities or higher dimension. In fact, Deninger [6] recently has extended the l-dimensional duality to the singular case, being then forced to take as a dualizing object a complex G of sheaves
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