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Supporting prerequisites · 03 — Spectral K-zero equality gives an actual projective stabilization
Presents 29 supporting prerequisites, covering dependency levels 12–26.
1 · Prerequisites
- Actual perfect Cartan through degree three on all qcqs field-schemes
- Rank and determinant on the second piece
- Motivic filtration and image groups
- Local free chains detect natural perfect operations on every qcqs base
- The globally normalized first-layer Picard map is determinant
- First Chern class factors through determinant
- External formal universal Chern maps and supported construction
- The Axiom of Choice
- The actual determinant fiber is a natural retract of the rank-zero K-space
- Flag towers with line-bundle quotients
- Detection on a simultaneous flag tower
- Filtration projections and multiplication
- Whitney identities and virtual Chern arithmetic
- The actual perfect K-space operations satisfy total Cartan
- Reduced bundle class identities
- Actual second-stage comparison on every qcqs field-scheme
- Graded filtration projections
- Stage projections, kernels and image groups
- Second Chern additivity on the second piece
- The stable free-class comparison is locally integrally acyclic
- Local integral chains detect global natural maps into Chern targets
- External actual universal-class detection on Vect and Grass
- Motivic projective bundle formula
- The actual first EM stage is the rank-zero K space on all qcqs schemes
- Elmanto–Morrow motivic complex input
- An actual non-A¹ P¹-spectrum for the supplied EM complexes
- Actual EM orientation and projective bundle maps on that model
- External symmetric P¹ model, orientation criterion and fundamental stabilization
- Negative coefficients of the actual EM projective-line model
- External actual graded algebra and multiplicative tower spectral sequence
- Annala–Iwasa, Motivic spectra and universality of K-theory, author PDF dated 14 April 2025 · Section 2.1 and Notations 2.2.7–2.2.9 / coefficient adjunction 2.2.10, pp. 14–15; Definition 4.4.1 through Corollary 4.4.7, pp. 30–32
- Asakura–Sato, Chern Class and Riemann–Roch Theorem for Cohomology Theory without Homotopy Invariance, J. Math. Sci. Univ. Tokyo 26 (2019) · Definition 5.1, Steps 1–3, Proposition 5.3, formula (5.3.1), and naturality square (5.4.1), pp. 269–272
- Elmanto–Morrow, Motivic cohomology of equicharacteristic schemes, arXiv:2309.08463v1 (15 September 2023 header; 18 September 2023 internal date) · Theorem 1.1 opening and part (1), printed p. 3
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
Apply the actual perfect Cartan identity to the second image
Lemma
The reduced universal bundle calculation identifies the second projection
Lemma
The perfect image filtration has the stated second projection and kernel
Lemma