Bredon sheaf cohomology computes algebraic K-theory of equivariant sheaves and equivariant E-theory of function algebras on G-spaces while satisfying a strong uniqueness theorem via open descent and compact codescent.
The six operations in topology, 2023
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The derived category of a locally compact Hausdorff space X is smooth if and only if X is discrete and finite.
Characterizes compact objects in Shv(X,C) for hypercomplete locally compact Hausdorff X and compactly generated stable C, recovering Neeman and showing compact generation iff X totally disconnected.
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Bredon sheaf cohomology
Bredon sheaf cohomology computes algebraic K-theory of equivariant sheaves and equivariant E-theory of function algebras on G-spaces while satisfying a strong uniqueness theorem via open descent and compact codescent.
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The derived category of a locally compact space is rarely smooth
The derived category of a locally compact Hausdorff space X is smooth if and only if X is discrete and finite.
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Compact sheaves on a locally compact space
Characterizes compact objects in Shv(X,C) for hypercomplete locally compact Hausdorff X and compactly generated stable C, recovering Neeman and showing compact generation iff X totally disconnected.