nLab simplicial scheme

Definition

A simplicial scheme is a simplicial object in a category of schemes.

References

• Bojan Mohar, Simplicial schemes, Journal of Combinatorial Theory, Series B Volume 42, Issue 1, February 1987, Pages 68–86, doi: 10.1016/0095-8956(87)90064-5, ScienceDirect

homotopy theory of simplicial schemes is discussed in

• David A. Cox, Homotopy theory and simplicial schemes, pdf-slides

• David A. Cox, Homotopy theory of simplicial schemes. Compositio Mathematica, 39 no. 3 (1979), p. 263-296 Full text djvu | pdf | Reviews MR 550644 | Zbl 0385.14004 stable URL

étale homotopy of simplicial schemes is discussed in

• Eric Friedlander, 1982, Étale homotopy of simplicial schemes , volume 104 of Annals of Mathematics Studies , Princeton University Press, Princeton, N.J.

motives in the context of simplicial schemes are discussed in

• V. Voevodsky, Motives over simplicial schemes, Journal of K-Theory, Volume 5, Issue 01 , pp 1 - 38,

  (preliminary version in K-theory preprint archive: here)

• Carlo Mazza, Vladimir Voevodsky, Charles Weibel, Lecture Notes on Motivic Cohomology, http://www.claymath.org/library/monographs/cmim02.pdf