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Chern constructions and support geometry
Develop flag detection and virtual Chern arithmetic alongside indexed support fibers, excision, Koszul classes and curve dévissage. Place the article's support definitions here and prepare the Bertini and exterior-Euler interfaces needed by its final geometric arguments.
1 · Prerequisites
- Exterior powers and determinant of an algebraic bundle
- Relative cofibers and quotient complexes
- Contravariant Hom reverses relative cofiber triangles
- Extending a Whitney class to K zero
- The Axiom of Choice
- Flag towers with line-bundle quotients
- Exterior Algebra Basis Monomials
- Grothendieck groups of coherent sheaves and of vector bundles on a scheme
- Kernels of surjections of vector bundles
- Unimodular elements and trivial summands
- Determinants and exact sequences
- Cohomology descends to the derived category
- Functorial finite coefficients for derived complexes
- Perfect complexes on schemes and their support
- External input on derived enhancements
- The Stacks Project, Derived Categories of Schemes · §36.11 introduction; Lemma 36.11.6(1); Lemma 36.11.8 and its proof
- Jacob Lurie, Higher Algebra · Definition 1.3.5.16 and Proposition 1.3.5.18 p. 128; Remark 1.3.5.19 and Proposition 1.3.5.21(2) p. 129
- Nisnevich covers and distinguished squares
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
Lemma
Dual conventions for the exterior Euler class
Lemma
Relative objects for empty and split pairs
Lemma
Formal Chern arithmetic through degree three
Lemma
Exterior-square line factors on a flag space
Lemma
Finite-dimensional families of generated bundle functionals
Lemma
A rank-two bundle with a trivial quotient and determinant
Lemma
Finite clopen common rank strata
Lemma
Line-quotient classes across clopen rank strata
Lemma
Finite derived products and motivic coefficient operations
Theorem
External regular perfection and the standard derived t structure
Lemma
Finite ideal-power filtrations and coherent sheaves on the closed subscheme
Lemma