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Vector bundles on singular surfaces and threefolds
The authors fully classify vector bundles of critical rank on normal affine surfaces and threefolds over algebraically closed fields via their Chern classes. The authors also prove existence of rank 2 bundles on threefolds with prescribed first and second motivic Chern classes.
The main input is the motivic filtration on algebraic K-theory: its third piece is generated by smooth closed points and is identified with motivic cohomology by the third Chern class.
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22 entriesPrerequisites
Affine bundles and normal geometry
Chern constructions and support geometry
Perfect K theory and motivic towers
Scheme sites and cycle theories
Supporting prerequisites · 01 — Localization sequence for Chow groups and homotopy invariance of affine space
Supporting prerequisites · 02 — Exact objectwise cofiber bound for the canonical source composite
Supporting prerequisites · 03 — Spectral K-zero equality gives an actual projective stabilization
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