The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.
Generators and representability of functors in commutative and noncommutative geometry
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abstract
We give a sufficient condition for an Ext-finite triangulated category to be saturated. Saturatedness means that every contravariant cohomological functor of finite type to vector spaces is representable. The condition consists in existence of a strong generator. We prove that the bounded derived categories of coherent sheaves on smooth proper commutative and noncommutative varieties have strong generators, hence saturated. In contrast the similar category for a smooth compact analytic surface with no curves is not saturated.
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2026 1verdicts
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Properties of deformed mass and phase functions
The paper proves continuity of deformed mass and phase functions on stability condition spaces, deduces a homeomorphic embedding into measures, and establishes a triangle inequality plus truncation estimates.