Abstract
We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also investigate the relationship of our result to path spaces in homotopy theory, Buchweitz-Flenner formality in algebraic geometry, and draw parallels with similar results in Lie theory and symplectic geometry.
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