Virtual excess intersection theory. (English) Zbl 1470.14018

Summary: We prove a \(K\)-theoretic excess intersection formula for derived Artin stacks. When restricted to classical schemes, it gives a refinement and new proof of R. W. Thomason’s [Invent. Math. 112, No. 1, 195–215 (1993; Zbl 0816.19004)] formula.


14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
14A30 Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.)
14A20 Generalizations (algebraic spaces, stacks)
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
19E08 \(K\)-theory of schemes


Zbl 0816.19004
Full Text: DOI arXiv


[1] 10.1090/conm/276/04519
[2] 10.1007/978-1-4612-1700-8
[3] 10.5802/ahl.55 · Zbl 1520.14047
[4] 10.1016/S0022-4049(02)00293-1 · Zbl 1078.14535
[5] ; Qu, Ann. Inst. Fourier (Grenoble), 68, 1609 (2018) · Zbl 1423.19009
[6] ; Grothendieck, Théorie des intersections et théorème de Riemann-Roch. Lecture Notes in Math., 225 (1971) · Zbl 0229.14008
[7] 10.1007/BF01232430 · Zbl 0816.19004
[8] 10.1007/s00222-002-0275-2 · Zbl 1032.19001
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