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Article items · 13 — Supported RR and the actual support-to-global application
Presents 29 items from the article and its immediate prerequisites, covering dependency levels 24–36.
1 · Prerequisites
- Positive supported coordinates at a smooth threefold point
- Actual supported Chern operation and its smooth comparison
- An integral P³ test fixes the supported RR coefficient as positive two
- The actual supported third edge sends the positive point class to its residue object
- External actual supported Riemann–Roch in codimension three
- Third edge homomorphism
- Third-stage graded isomorphism
- The Axiom of Choice
- Normal dimension strata and the actual residue class model
- Finite clopen restrictions split the actual motivic image filtration
- Perfect K theory localization and open excision
- Elmanto–Morrow motivic complex input
- Derived Nisnevich descent on a finite clopen partition
- Motivic graded pieces and spectral sequence
- Motivic filtration and image groups
- Graded filtration projections
- The actual first EM stage is the rank-zero K space on all qcqs schemes
- Canonical first motivic class on every perfect K zero class
- First Chern class factors through determinant
- Motivic weight one
- Smooth-locus restriction properties
- Smooth rank, first Chern, determinant and supported positive leading cycle
- The actual determinant fiber is a natural retract of the rank-zero K-space
- Whitney identities and virtual Chern arithmetic
- Actual perfect Cartan through degree three on all qcqs field-schemes
- The globally normalized first-layer Picard map is determinant
- Stage projections, kernels and image groups
- Subgroup generated by smooth closed points
- Levine–Weibel cycle image with pure-dimensional and component conventions
- Dimension-specific point images and a precise lower-component obstruction
- Divisibility of an image with torsion kernel
- Unique divisibility is invariant under group isomorphism
- Krishna's affine zero-cycle divisibility and kernel input
- Units and Picard groups in Nisnevich degree zero and one
- Determinant descends on the actual perfect K zero
- Actual second-stage comparison on every qcqs field-scheme
- Rank-three alternating exterior class
- Affine bundles and finite projective modules
- Affine perfect K zero and bundle K zero
- The actual exterior-dual class in affine perfect K zero
- Murthy splitting criterion for the exterior-dual obstruction
- Formal Chern arithmetic through degree three
- The perfect image filtration has the stated second projection and kernel
- High filtration vanishing
- Article scheme conventions
- Motivic splitting principle
- Exterior-square line factors on a flag space
- The actual perfect K-space operations satisfy total Cartan
- External formal universal Chern maps and supported construction
- Zeroth projection is rank
- Low-stage homotopy equals its image
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · PDF p. 12, proof of Theorem A; p. 17, proof of Theorem B
- Critical-rank representatives of rank-zero classes
- Bertini functional with finite smooth zero locus
- Bertini curve functional with a prescribed avoidance locus
- Determinants and exact sequences
- A rank-two bundle with a trivial quotient and determinant
- Nonconnective K theory of perfect complexes
- Serre splitting above the dimension
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · PDF p. 12, final paragraph of the proof of Theorem A
- Excision and K theory purity at a smooth closed point
- Motivic purity and lower-weight vanishing at a smooth closed point
- Smooth point classes lie in the top filtration piece
- Motivic and filtered K theory with support
- Support fibers commute with graded triangles
- Open excision for a descent theory
- Isomorphism classes of vector bundles
- First-class matching and explicit perfect Chern arithmetic
- Critical-rank cancellation used in the article
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · Abstract; PDF p. 2, Theorem A and following paragraph; p. 12, proof of Theorem A
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · PDF p. 2, paragraph following Theorem A
- Third edge isomorphism
- Third edge on a curve complement
- Generic localization detects the point subgroup
- Perfect residue classes at smooth closed points
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · PDF p. 1, abstract; p. 17, Corollary 6.9 and proof
- Motivic Chern classes
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · PDF p. 17, proof of Theorem B, surjectivity
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · PDF p. 1, abstract; p. 2, Theorem B; p. 17, proof of Theorem B
- Jean Fasel and Maria Yakerson, Vector bundles on singular surfaces and threefolds · PDF p. 1, abstract; p. 3, Corollary D; p. 17, Corollary 6.10 and its proof
2 · Logical flowchart
Arrows show item dependencies. A grouped prerequisite node points to items that use one or more of its members; their exact links are listed above.
3 · Items
LemmaDependency level 24
Supported RR and the actual support-to-global application
LemmaDependency level 24
First projection is first Chern class
LemmaDependency level 24
Reduced bundle class identities
LemmaDependency level 24
Second Chern additivity on the second piece
LemmaDependency level 24
Rank and determinant on the second piece
PropositionDependency level 24
Unique divisibility of the smooth-point subgroup
TheoremDependency level 24
Line bundles and first motivic Chern class
LemmaDependency level 25
The first two perfect Chern classes vanish on the third image piece in full scope
PropositionDependency level 25
Murthy splitting input in rank three
PropositionDependency level 25
Factor two in the supported third Chern map
LemmaDependency level 26
Degree-three coefficient algebra on the lower-Chern kernel
LemmaDependency level 26
The low-dimensional quotient follows from the stage sequence
LemmaDependency level 27
Third Chern additivity on the third piece
PropositionDependency level 27
Second projection is minus second Chern class
LemmaDependency level 28
Chern classes of the alternating exterior class
LemmaDependency level 28
Second Chern surjectivity in dimensions two and three
LemmaDependency level 28
Rank-three representatives with two zero Chern classes
LemmaDependency level 29
Curve-and-point support reduction
LemmaDependency level 29
Prescribing two surface Chern classes
LemmaDependency level 30
Removing isolated points from the support
TheoremDependency level 30
Motivic Chern classification on normal affine surfaces
CorollaryDependency level 31
Independent determinant and second-Chern prescription
LemmaDependency level 31
Lifting the corrected class to the curve-supported third stage
TheoremDependency level 32
Smooth points generate the third motivic piece
CorollaryDependency level 33
Third Chern isomorphism
CorollaryDependency level 34
Third Chern vanishing and a trivial summand
LemmaDependency level 34
Prescribing three Chern classes successively
TheoremDependency level 35
Motivic Chern classification on normal affine threefolds
CorollaryDependency level 36