2018/10/09 by Mantovani, Lorenzo
#14F42 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1810.04134
Let K be a perfect field and let E be a homotopy commutative ring spectrum in the Morel-Voevodsky stable motivic homotopy category SH(K). In this work we investigate the relation between the E-homology localization and E-nilpotent completion of a spectrum X. Under reasonable assumptions on E and X we show that these two operations coincide and can be expressed in terms of formal completions or localizations in the usual sense of commutative algebra. We deduce convergence criteria for the E-based motivic Adams-Novikov spectral sequence.