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Supporting prerequisites · 02 — Exact objectwise cofiber bound for the canonical source composite
Presents 28 supporting prerequisites, covering dependency levels 1–11.
1 · Prerequisites
- External EM multiplicative motivic complexes and actual Chern map
- Elden Elmanto and Matthew Morrow, Motivic cohomology of equicharacteristic schemes (arXiv v1) · Theorem5.24(2), p.43, and its proof pp.43–44; preceding explicit component maps and line convention, p.43; Definition5.2 and negative-weight convention following(5.2), p.34
- The Axiom of Choice
- External canonical field restriction identifies the BEM and EM cdh models
- Bachmann–Elmanto–Morrow, A¹-invariant motivic cohomology of schemes, served v1 HTML · Theorem 7.5, Definition 7.8, Remark 7.9; comparison (1.9), Corollary 1.11; proof of Theorem 6.3, paragraphs preceding and following (6.4)
- Mazza–Voevodsky–Weibel, Lecture notes on motivic cohomology, Rutgers served PDF · Printed p.126, Theorem 16.7; printed pp.159–163, Lemma 19.4, Theorem 19.8, Proposition 19.12, Definition 19.13 and Example 19.14 (PDF pp.138–139 and 171–175)
- Full projective Quillen–Waldhausen comparison and the local free-class map
- External connective, nonconnective and automorphism comparisons
- Bounded finite-projective complexes and affine chain models
- Enhanced affine perfect equivalence
- Affine perfect K zero and bundle K zero
- Nonconnective K theory of perfect complexes
- Scheme sites and sheafification
- Charles Weibel, The K-book, Chapters IV and V · V.2.2 and proof, pp. 13–14; V.2.7.2, p. 18; canonical S/Q comparison IV.8.5–8.7, pp. 74–75 in Kbook.IV.pdf
- Charles Weibel, The K-book, author-hosted Chapter IV · IV.8.3.2 and IV.8.5, p. 68; Exercises IV.8.5–8.7, pp. 74–75
- Blumberg–Gepner–Tabuada, A universal characterization of higher algebraic K-theory, arXiv:1001.2282v4 · Lemma 7.11/Corollary 7.12, pp. 48–49; Proposition 9.32 and Remark 9.33, p. 64; Definition 9.6/Theorem 9.8, p. 58
- Asakura–Sato, Chern Class and Riemann–Roch Theorem for Cohomology Theory without Homotopy Invariance, 2019 · Definition 5.1 and §5 Steps 1–3, printed pp. 269–271
- Jacob Lurie, Higher Topos Theory, author-hosted PDF (accessed 9 November 2026) · Proposition 6.2.2.7, printed p. 579, proof pp. 582–583; paragraph following Proposition 6.5.2.8, printed p. 669 (PDF p. 687)
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
Theorem
External EM projective bundle equivalence with its specified components
Theorem
Fixed-site classical cycle comparison on every smooth ambient
Lemma