133 citations · 504 across the 25 of their papers we have counts for
25 papers · 1 filter
Grothendieck-Witt theory of derived schemes
Marc Hoyois, Markus Land
We construct a non--invariant motivic ring spectrum over , whose associated cohomology theory on qcqs derived schemes is the…
Remarks on the motivic sphere without -invariance
Marc Hoyois
We generalize several basic facts about the motivic sphere spectrum in -homotopy theory to the category of non--invariant motivic spectra ov…
Atiyah duality for motivic spectra
Toni Annala, Marc Hoyois, Ryomei Iwasa
We prove that Atiyah duality holds in the -category of non--invariant motivic spectra over arbitrary derived schemes: every smooth projective scheme is dualiza…
Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory
Toni Annala, Marc Hoyois, Ryomei Iwasa
We formulate and prove a Conner-Floyd isomorphism for the algebraic K-theory of arbitrary qcqs derived schemes. To that end, we study a stable -category of non-$\mathbb A^1…
Introduction to Framed Correspondences
Marc Hoyois, Nikolai Opdan
We give an overview of the theory of framed correspondences in motivic homotopy theory. Motivic spaces with framed transfers are the analogue in motivic homotopy theory of $E_{\inf…
Hermitian K-theory via oriented Gorenstein algebras
Marc Hoyois, Joachim Jelisiejew, Denis Nardin +1
We show that the hermitian K-theory space of a commutative ring R can be identified, up to A^1-homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-a…
Milnor excision for motivic spectra
Elden Elmanto, Marc Hoyois, Ryomei Iwasa +1
We prove that the -category of motivic spectra satisfies Milnor excision: if is a morphism of commutative rings sending an ideal isomorphically onto a…
Cdh descent, cdarc descent, and Milnor excision
Elden Elmanto, Marc Hoyois, Ryomei Iwasa +1
We give necessary and sufficient conditions for a cdh sheaf to satisfy Milnor excision, following ideas of Bhatt and Mathew. Along the way, we show that the cdh infinity-topos of a…
The Hilbert scheme of infinite affine space and algebraic K-theory
Marc Hoyois, Joachim Jelisiejew, Denis Nardin +2
We study the Hilbert scheme from an -homotopical viewpoint and obtain applications to algebraic K-theory. We show that the Hilber…
On the infinite loop spaces of algebraic cobordism and the motivic sphere
Tom Bachmann, Elden Elmanto, Marc Hoyois +3
We obtain geometric models for the infinite loop spaces of the motivic spectra , , and over a field. They are motivically equivalent to $\m…
Modules over algebraic cobordism
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We prove that the -category of -modules over any scheme is equivalent to the -category of motivic spectra with finite syntomic transfers. Using the re…
The étale symmetric Künneth theorem
Marc Hoyois
Let be an algebraically closed field, a prime number, and a quasi-projective scheme over . We show that the étale homotopy type of the th…
Framed transfers and motivic fundamental classes
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We relate the recognition principle for infinite -loop spaces to the theory of motivic fundamental classes of Déglise, Jin, and Khan. We first compare two kinds of tra…
Affine representability results in A^1-homotopy theory III: finite fields and complements
Aravind Asok, Marc Hoyois, Matthias Wendt
We give a streamlined proof of -representability for -torsors under "isotropic" reductive groups, extending previous results in this sequence of papers to finite…
The localization theorem for framed motivic spaces
Marc Hoyois
We prove the analog of the Morel-Voevodsky localization theorem for framed motivic spaces. We deduce that framed motivic spectra are equivalent to motivic spectra over arbitrary sc…
Motivic infinite loop spaces
Elden Elmanto, Marc Hoyois, Adeel A. Khan +2
We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic anal…
Norms in motivic homotopy theory
Tom Bachmann, Marc Hoyois
If is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor , where $\mathcal H_*…
Generically split octonion algebras and A^1-homotopy theory
Aravind Asok, Marc Hoyois, Matthias Wendt
We study generically split octonion algebras over schemes using techniques of -homotopy theory. By combining affine representability results with techniques of obstr…
The six operations in equivariant motivic homotopy theory
Marc Hoyois
We introduce and study the homotopy theory of motivic spaces and spectra parametrized by quotient stacks [X/G], where G is a linearly reductive linear algebraic group. We extend to…
Affine representability results in A^1-homotopy theory II: principal bundles and homogeneous spaces
Aravind Asok, Marc Hoyois, Matthias Wendt
We establish a relative version of the abstract "affine representability" theorem in --homotopy theory from Part I of this paper. We then prove some -…
Affine representability results in -homotopy theory I: vector bundles
Aravind Asok, Marc Hoyois, Matthias Wendt
We establish a general "affine representability" result in -homotopy theory over a general base. We apply this result to obtain representability results for vector b…
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.
A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
Marc Hoyois
We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the "Euler characteristi…
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…