Relative cycle
In-game article clicks load inline without leaving the challenge.
In algebraic geometry, a relative cycle is a type of algebraic cycle on a scheme. In particular, let X {\displaystyle X} be a scheme of finite type over a Noetherian scheme S {\displaystyle S}, so that X → S {\displaystyle X\rightarrow S}. Then a relative cycle is a cycle on X {\displaystyle X} which lies over the generic points of S {\displaystyle S}, such that the cycle has a well-defined specialization to any fiber of the projection X → S {\displaystyle X\rightarrow S}.(Voevodsky & Suslin 2000)
The notion was introduced by Andrei Suslin and Vladimir Voevodsky in 2000; the authors were motivated to overcome some of the deficiencies of sheaves with transfers.
- Cisinski, Denis-Charles; Déglise, Frédéric (2019). Triangulated Categories of Mixed Motives. Springer Monographs in Mathematics. arXiv:. doi:. ISBN978-3-030-33241-9. S2CID.
- Voevodsky, Vladimir; Suslin, Andrei (2000). "Relative cycles and Chow sheaves". Cycles, Transfers and Motivic Homology Theories. Annals of Mathematics Studies, vol. 143. Princeton University Press. pp.10–86. ISBN9780691048147. OCLC.
- Appendix 1A of Mazza, Carlo; Voevodsky, Vladimir; Weibel, Charles (2006), Lecture notes on motivic cohomology, Clay Mathematics Monographs, vol.2, Providence, R.I.: American Mathematical Society, ISBN978-0-8218-3847-1, MR