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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
- Exact true-triangle and Waldhausen determinant one-type input
- Nonconnective K theory of perfect complexes
- Bounded finite-projective complexes and affine chain models
- External connective, nonconnective and automorphism comparisons
- The Axiom of Choice
- Units and Picard groups in Nisnevich degree zero and one
- Dévissage of K zero with regular ambient support
- Noetherian devissage for coherent proper pushforward
- Coherent sheaves on a locally Noetherian scheme
- A coherent closed-point skyscraper
- Bottom supported Bloch groups on a codimension two curve
- Augmented tower comparisons preserve supported graded projections
- Support fibers commute with graded triangles
- Motivic and filtered K theory with support
- Motivic filtration and image groups
- Affine perfect K zero and bundle K zero
- Units split the K one determinant
- Finn Knudsen and David Mumford, The projectivity of the moduli space of stable curves I: Preliminaries on det and Div · Chapter I pp.20–21,31; Definition2 p.37 and remark p.38; Definition4 pp.40–42 including p.41 footnote; Theorem2 p.42; Corollary2 p.43 and warning p.44
- Charles Weibel, The K-book · Example IV.4.4.2, p.39; together with Chapter II §2 (local K₀=Z) and Chapter III Lemma1.4 (commutative semilocal K₁=units)
- Charles Weibel, The K-book, Chapter V, contextual descent statement · §10 introduction and Example10.3, p.72; Nisnevich discussion and Theorem10.10, p.76; Example10.10.1, p.77
- Jacob Lurie, Higher Topos Theory · Proposition 7.2.2.12(2) and displayed proof; Remark7.2.2.13 and Definition7.2.2.14
- Perfect K theory localization and open excision
- External EM low-weight maps with fixed positive normalization
- Weight zero is the locally constant rank function
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
The actual graded determinant map on the current K-space
Lemma
Generic rank and point-supported classes on a curve
Lemma
The supported second stage has the actual augmentation inverse
Theorem
External determinant and pointed one-type inputs
Lemma
The actual supported Euler class has the generic length coordinate
Lemma
The EM weight-one Picard normalization is positive identity
Lemma
Positive generic cycles determine the curve-supported homomorphism
Lemma