133 citations · 504 across the 25 of their papers we have counts for
34 papers
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…
Remarks on étale motivic stable homotopy theory
Tom Bachmann, Marc Hoyois
We strengthen some results in étale (and real étale) motivic stable homotopy theory, by eliminating finiteness hypotheses, additional localizations and/or extending to spectra from…
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…
The categorified Grothendieck-Riemann-Roch theorem
Marc Hoyois, Pavel Safronov, Sarah Scherotzke +1
In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for Toën and Vezzosi's seco…
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_*…
Vanishing theorems for the negative K-theory of stacks
Marc Hoyois, Amalendu Krishna
We prove that the homotopy algebraic K-theory of tame quasi-DM stacks satisfies cdh-descent. We apply this descent result to prove that if X is a Noetherian tame quasi-DM stack and…
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…
Topoi of parametrized objects
Marc Hoyois
We give necessary and sufficient conditions on a presentable infinity-category C so that families of objects of C form an infinity-topos. In particular, we prove a conjecture of Jo…
Categorifying rationalization
Clark Barwick, Saul Glasman, Marc Hoyois +2
We solve a problem proposed by Khovanov by constructing, for any set of primes , a triangulated category (in fact a stable -category) whose Grothendieck group is $S^{-1}…
Cdh descent in equivariant homotopy K-theory
Marc Hoyois
We construct geometric models for classifying spaces of linear algebraic groups in G-equivariant motivic homotopy theory, where G is a tame group scheme. As a consequence, we show…