2003/08/20 by Vasiu, Adrian
#11G10 #11G18 #11S25 #14F30 #14G35 #14L05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #and 20G25
paper · doi:10.48550/arxiv.math/0308202
Let k be an algebraically closed field of characteristic p>0. Let W(k) be the ring of Witt vectors with coefficients in k. We prove a motivic conjecture of Milne that relates, in the case of abelian schemes, the étale cohomology with \dbZp coefficients to the crystalline cohomology with integral coefficients, in the more general context of p-divisible groups endowed with \it arbitrary families of crystalline tensors over a finite, discrete valuation ring extension of W(k). This extends a result of Faltings in [Fa2]. As a main new tool we construct global deformations of p-divisible groups endowed with crystalline tensors over certain regular, formally smooth schemes over W(k) whose special fibers over k have a Zariski dense set of k-valued points.