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