GENERALIZED t-STRUCTURES: t-STRUCTURES FOR SHEAVES OF DG-MODULES OVER A SHEAF OF DG-ALGEBRAS AND DIAGONAL t-STRUCTURES
نویسنده
چکیده
t-structures, in the abstract, apply to any triangulated category. However, for the most part, they have been studied so far only in the context of sheaves of modules over sites provided with sheaves of rings. In this paper we define and study t-structures for categories of modules over sites provided with sheaves of dgas and E∞-dgas. A close variant, as we show, are the diagonal t-structures that come up in the context of crystalline cohomology (as in the work of Ekedahl). All of this is carried out in the unified frame-work of aisles. We conclude with several examples: `-adic equivariant derived categories of toric varieties, the diagonal t-structures in crystalline derived categories as well as t-structures on motivic derived categories that are compatible with étale realization.
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