Alphabeta MathPersonal research
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
- Projective bundle in the quotient convention
- Picard group of a scheme
- The Axiom of Choice
- Elden Elmanto and Matthew Morrow, Motivic cohomology of equicharacteristic schemes, arXiv:2309.08463v1 PDF · Theorem 5.24(2), printed/PDF p.43; introductory projectivization convention immediately above; final proof paragraph p.44. Negative-weight zero convention in Section 5.1 immediately before Theorem 5.3, p.34.
- Derived category of an abelian category
- Long exact Hom sequences of a distinguished triangle
- Charles A. Weibel, The K-book: An Introduction to Algebraic K-theory, Chapter II: The Grothendieck Group K₀ · §II.6, Dévissage Theorem 6.3, printed and PDF p. 50; proof on the same page
- Bruno Kahn and Marc Levine, Motives of Azumaya algebras, JIMJ 9 (2010), 481–599, published final PDF · Notation p.487; Proposition 2.2.2 p.496 and compatible tower diagram p.498; Lemmas 2.3.1–2.3.2 pp.499–500; Definition 3.1.5 p.503.
- Kahn–Levine, published construction of the cycle map and its K/G comparison · Definitions 3.1.9–3.1.15 pp.505–507; Theorem 3.2.4 and its complete proof pp.508–510; Lemma 6.2.1 p.535; Lemmas 6.4.1–6.4.3 pp.539–540.
- Kahn–Levine, positive cycle coefficient and face convention · Section 5.9, printed pp.531–532, before Lemma 5.9.1; for orientation context Theorem 6.5.5 and its proof pp.542–543.
- Marc Levine, The homotopy coniveau tower, arXiv math/0510334v1 · Section8.3 pp.46–47, equation(8.3.1); Theorem9.0.3 and Remark9.0.4 p.47; model conventions pp.44–45
- Knudsen–Mumford, The projectivity of the moduli space of stable curves I: Preliminaries on det and Div · graded invertible sheaves pp20–21; alternating determinant p31; Definition2 p37 and remark p38; Definition4 pp40–42 including footnote p41; Theorem2 p42; warning and Proposition7 p44
- Fernando Muro, Andrew Tonks and Malte Witte, On determinant functors and K-theory, Publicacions Matematiques59(2015),137–233 · Definition1.2.3 and axioms pp145–146; Example1.2.7 p147; Definition1.2.9 pp147–148; Theorem1.5.4 pp161–162; section1.6 Lemma1.6.1 p166 and Theorem1.6.3 p167; natural construction statement surrounding Theorem4.3.4 p212
- Blumberg–Gepner–Tabuada, A universal characterization of higher algebraic K-theory · Lemma7.11 and Corollary7.12 pp48–49; Remark9.33 p64; compare completed enhanced-comparison supplier
- Projective bundle represents line quotients
- Kernels of surjections of vector bundles
- Relative projective space from standard charts
- The relative projective-space diagonal is closed
- Grothendieck groups of coherent sheaves and of vector bundles on a scheme
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
Definition
Bigraded cohomology and the projective bundle contract
Theorem
External projective bundle input for the actual motivic complex
Lemma
Relative cofibers and quotient complexes
Lemma
Contravariant Hom reverses relative cofiber triangles
Lemma
Purity twists and cohomological shifts with explicit premises
Theorem
External degree-zero abelian dévissage
Theorem
External supported slice projection with positive generic coefficient
Theorem
Exact true-triangle and Waldhausen determinant one-type input
Lemma
Projective bundle pullback detects cohomology classes
Lemma
Flag towers with line-bundle quotients
Lemma
Chern coefficients of the projective relation
Lemma