Algebraic computations in derived categories

Derived Algebraic Geometry I: Stable ∞-Categories

Derived Algebraic Geometry I: Stable ∞-Categories

DERIVED l-ADIC CATEGORIES FOR ALGEBRAIC STACKS

We construct an l-adic formalism of derived categories for algebraic stacks. Over finite fields we generalize the theory of mixed complexes to a theory of so called convergent complexes. This leads to a proof of the Lefschetz Trace Formula for the Frobenius.

Derived Algebraic Geometry I: Stable ∞-Categories

ON ALGEBRAIC AND COALGEBRAIC CATEGORIES OF VARIETY-BASED TOPOLOGICAL SYSTEMS

Motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by S. Vickers, providing an algebraic and a coalgebraic category of the new structures. As a result, the nature of the category   TopSys   of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...