2014/03/08 by Amalendu Krishna, Krishna, Amalendu, Paul Arne Østvær +2 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14L30 #msc:55P91
paper · pdf · doi:10.48550/arxiv.1403.1915
44 pages
arxiv created 2014/03/08 · arxiv updated 2014/03/11
To smooth schemes equipped with a smooth affine group scheme action, we associate an equivariant motivic homotopy category. Underlying our construction is the choice of an `equivariant Nisnevich topology' induced by a complete, regular, and bounded cd-structure. We show equivariant K-theory of smooth schemes is represented in the equivariant motivic homotopy category. This is used to characterize equivariantly contractible smooth affine curves and equivariant vector bundles on such curves. Generalizations of the purity and blow-up theorems in motivic homotopy theory are shown for actions of finite cyclic groups.