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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
- Cycle complexes with fixed support
- The dimension formula for affine domains
- The Axiom of Choice
- Finite clopen common rank strata
- Derived Nisnevich descent on a finite clopen partition
- Finite derived products and motivic coefficient operations
- Motivic complexes and cohomology
- Elmanto–Morrow motivic complex input
- Flag towers with line-bundle quotients
- Projective bundle pullback detects cohomology classes
- Bigraded cohomology and the projective bundle contract
- Line-quotient classes across clopen rank strata
- External projective bundle input for the actual motivic complex
- Perfect complexes on schemes and their support
- Nonconnective K theory of perfect complexes
- Nonconnective K theory in degree zero
- Regular equals smooth over a perfect field
- regular local residue field koszul resolution
- regular local rings are domains and cohen macaulay
- Finite-variable polynomial algebras over fields are Noetherian by finite generators
- External regular perfection and the standard derived t structure
- Cofiber and triangle presentations of K zero
- Derived global sections on a scheme site
- Complex shifts and spectral homotopy indices
- Exterior powers and determinant of an algebraic bundle
- Koszul Complex Resolves A Regular Quotient
- Koszul Complex Of A Sequence With Coefficients
- Isomorphism classes of vector bundles
- Motivic filtration and image groups
- Elden Elmanto and Matthew Morrow, Motivic cohomology of equicharacteristic schemes · Theorem3.5(8) in weight zero; Examples 4.11/4.26 and Construction4.36; Construction 5.5; Lemmas 5.10 and 5.12, especially (5.8); Lemma 5.1/Definition 5.2; Theorem 5.3; Corollary 7.11
- Elden Elmanto and Matthew Morrow, Motivic cohomology of equicharacteristic schemes · Construction4.34 (4.8)–(4.9); Construction4.36; Theorem6.1(2), Remark6.3 and Corollary6.4; Theorem3.5(1),(8) and Remark3.6, pp.14–16; footnote12 p.45
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
Bottom supported Bloch groups on a codimension two curve
Lemma
Finite rank strata detect Elmanto-Morrow motivic cohomology
Lemma
Detection on a simultaneous flag tower
Lemma
Perfect residue classes at smooth closed points
Lemma
Inherited bounded t structure on supported perfect complexes
Lemma
Additivity of the supported coherent Euler class
Definition
Support fibers with explicit cohomological indexing
Lemma
Euler class of a regular bundle functional
Lemma
Postnikov inverse and the specified nonconnective degree-zero group
Theorem
External EM low-weight maps with fixed positive normalization
Theorem