43 citations · 129 across the 22 of their papers we have counts for
8 papers · 1 filter
Vanishing in stable motivic homotopy sheaves
Kyle Ormsby, Oliver Röndigs, Paul Arne Østvær
We determine systematic regions in which the bigraded homotopy sheaves of the motivic sphere spectrum vanish.
The first stable homotopy groups of motivic spheres
Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær
We compute the 1-line of stable homotopy groups of motivic spheres over fields of characteristic not two in terms of hermitian and Milnor K-groups. This is achieved by solving ques…
Topological comparison theorems for Bredon motivic cohomology
Jeremiah Heller, Mircea Voineagu, Paul Arne Ostvaer
We prove equivariant versions of the Beilinson-Lichtenbaum conjecture for Bredon motivic cohomology of smooth complex and real varieties with an action of the group of order two. T…
Two-complete stable motivic stems over finite fields
Glen M. Wilson, Paul Arne Østvær
Let be a prime and where is a prime different from . We show that the -completion of the th stable homotopy group of spheres is a summand of the…
Motivic homotopy theory of group scheme actions
Jeremiah Heller, Amalendu Krishna, Paul Arne Ostvaer
We define an unstable equivariant motivic homotopy category for an algebraic group over a Noetherian base scheme. We show that equivariant algebraic -theory is representable in…
Stable motivic pi_1 of low-dimensional fields
Kyle M. Ormsby, Paul Arne Østvær
Let k be a field with cohomological dimension less than 3; we call such fields low-dimensional. Examples include algebraically closed fields, finite fields and function fields ther…
Motivic Brown-Peterson invariants of the rationals
Kyle M. Ormsby, Paul Arne Østvær
Fix the base field Q of rational numbers and let BP<n> denote the family of motivic truncated Brown-Peterson spectra over Q. We employ a "local-to-global" philosophy in order to co…
Motivic twisted K-theory
Markus Spitzweck, Paul Arne Østvær
This paper sets out basic properties of motivic twisted K-theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K-theory is defined in terms…