43 citations · 129 across the 22 of their papers we have counts for
28 papers
The logarithmic - and -topologies
Nikolai Opdan, Doosung Park, Paul Arne Østvær
We introduce the - and -topologies in the context of logarithmic geometry and discuss their applications to log étale cohomology, log differential forms, and log motives.
On the logarithmic slice filtration
Federico Binda, Doosung Park, Paul Arne Østvær
We consider slice filtrations in logarithmic motivic homotopy theory. Our main results establish conjectured compatibilities with the Beilinson, BMS, and HKR filtrations on (topolo…
Logarithmic Prismatic Cohomology via Logarithmic THH
Federico Binda, Tommy Lundemo, Doosung Park +1
Inspired by Bhatt-Morrow-Scholze's work on , we define Nygaard-completed log prismatic cohomology based on log topological Hochschild homology via filtrations on log ${\…
The Multiplicative Structures on Motivic Homotopy Groups
Daniel Dugger, Bjørn Ian Dundas, Daniel C. Isaksen +1
We reconcile the multiplications on the homotopy rings of motivic ring spectra used by Voevodsky and Dugger. While the connection is elementary and similar phenomena have been obse…
A Hochschild-Kostant-Rosenberg theorem and residue sequences for logarithmic Hochschild homology
Federico Binda, Tommy Lundemo, Doosung Park +1
This paper incorporates the theory of Hochschild homology into our program on log motives. We discuss a geometric definition of logarithmic Hochschild homology of derived pre-log r…
Bredon motivic cohomology of the complex numbers
Jeremiah Heller, Mircea Voineagu, Paul Arne Østvær
Over the complex numbers, we compute the -equivariant Bredon motivic cohomology ring with coefficients. By rigidity, this extends Suslin's calculation of the mo…
Geometric models for algebraic suspensions
Aravind Asok, Adrien Dubouloz, Paul Arne Østvær
We analyze the question of which motivic homotopy types admit smooth schemes as representatives. We show that given a pointed smooth affine scheme and an embedding into affine…
Topological models for stable motivic invariants of regular number rings
Tom Bachmann, Paul Arne Østvær
For an infinity of number rings we express stable motivic invariants in terms of topological data determined by the complex numbers, the real numbers, and finite fields. We use thi…
Milnor-Witt Motives
Tom Bachmann, Baptiste Calmès, Frédéric Déglise +2
We develop the theory of Milnor-Witt motives and motivic cohomology. Compared to Voevodsky's theory of motives and his motivic cohomology, the first difference appears in our defin…
Algebraic Cobordism and Étale Cohomology
Elden Elmanto, Marc Levine, Markus Spitzweck +1
Thomason's étale descent theorem for Bott periodic algebraic -theory \cite{aktec} is generalized to any module over a regular Noetherian scheme of finite dimension. Over a…
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 motivic Hopf map solves the homotopy limit problem for -theory
Oliver Röndigs, Markus Spitzweck, Paul Arne Østvær
We solve affirmatively the homotopy limit problem for -theory over fields of finite virtual cohomological dimension. Our solution employs the motivic slice filtration and the fi…
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…
A1-contractibility of Koras-Russell threefolds
Marc Hoyois, Amalendu Krishna, Paul Arne Østvær
Finite suspensions of Koras-Russell threefolds are contractible in A1-homotopy theory.
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…
Motivic homotopy of group scheme actions
Amalendu Krishna, Paul Arne Ostvaer
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 `equivar…
Slices of hermitian K-theory and Milnor's conjecture on quadratic forms
Oliver Röndigs, Paul Arne Østvær
We advance the understanding of K-theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K-groups and Witt-groups. By an explicit computati…
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…
The motivic Steenrod algebra in positive characteristic
Marc Hoyois, Shane Kelly, Paul Arne Østvær
Let S be an essentially smooth scheme over a field and l a prime number invertible on S. We show that the algebra of bistable operations in the mod l motivic cohomology of smooth S…
Equivariant cycles and cancellation for motivic cohomology
Jeremiah Heller, Mircea Voineagu, Paul Arne Ostvaer
We introduce a Bredon motivic cohomology theory for smooth schemes defined over a field and equipped with an action by a finite group. These cohomology groups are defined for finit…
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 slices and colored operads
Javier J. Gutiérrez, Oliver Röndigs, Markus Spitzweck +1
Colored operads were introduced in the 1970's for the purpose of studying homotopy invariant algebraic structures on topological spaces. In this paper we introduce colored operads…