43 citations · 129 across the 22 of their papers we have counts for
15 papers · 1 filter
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…
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…
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 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…
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 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…
Existence and uniqueness of E-infinity structures on motivic K-theory spectra
Niko Naumann, Markus Spitzweck, Paul Arne Østvær
We show that algebraic K-theory KGL, the motivic Adams summand ML and their connective covers acquire unique E-infinity structures refining naive multiplicative structures in the m…