On the infinite loop spaces of algebraic cobordism and the motivic sphere

Autor: Tom Bachmann, Elden Elmanto, Marc Hoyois, Adeel A. Khan, Vladimir Sosnilo, Maria Yakerson

Publikováno v: Épijournal de Géométrie Algébrique, Vol Volume 5 (2021)

We obtain geometric models for the infinite loop spaces of the motivic spectra $\mathrm{MGL}$, $\mathrm{MSL}$, and $\mathbf{1}$ over a field. They are motivically equivalent to $\mathbb{Z}\times \mathrm{Hilb}_\infty^\mathrm{lci}(\mathbb{A}^\infty)^+$

Externí odkaz: https://doaj.org/article/c33b7305e536426480166b1e6e37b025

CATEGORIFYING RATIONALIZATION

Autor: CLARK BARWICK, SAUL GLASMAN, MARC HOYOIS, DENIS NARDIN, JAY SHAH

Publikováno v: Forum of Mathematics, Sigma, Vol 7 (2019)

We construct, for any set of primes $S$, a triangulated category (in fact a stable $\infty$-category) whose Grothendieck group is $S^{-1}\mathbf{Z}$. More generally, for any exact $\infty$-category $E$, we construct an exact $\infty$-category $S^{-1}

Externí odkaz: https://doaj.org/article/cc111a5a43e64d94adcaa3ae98012985

Cdh descent, cdarc descent, and Milnor excision

Autor: Elden Elmanto, Marc Hoyois, Shane Kelly, Ryomei Iwasa

Publikováno v: Elmanto, E, Hoyois, M, Iwasa, R & Kelly, S 2021, ' Cdh descent, cdarc descent, and Milnor excision ', Mathematische Annalen, vol. 379, pp. 1011–1045 . https://doi.org/10.1007/s00208-020-02083-5

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 quasi-compact quasi-separated scheme of finite valuative dimension is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::48e9a5fb9a20a92c76fa426fc912fb40
https://doi.org/10.1007/s00208-020-02083-5

Framed transfers and motivic fundamental classes

Autor: Marc Hoyois, Adeel A. Khan, Vladimir Sosnilo, Elden Elmanto, Maria Yakerson

Publikováno v: Journal of Topology. 13:460-500

We relate the recognition principle for infinite $\mathbf P^1$-loop spaces to the theory of motivic fundamental classes of D\'eglise, Jin, and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ca5d714f70a9da8d8f1dec6d0c4dd39b
https://doi.org/10.1112/topo.12134

The categorified Grothendieck-Riemann-Roch theorem

Autor: Pavel Safronov, Nicolò Sibilla, Marc Hoyois, Sarah Scherotzke

Publikováno v: Hoyois, M, Safronov, P, Scherotzke, S & Sibilla, N 2021, ' The categorified Grothendieck-Riemann-Roch theorem ', Compositio Mathematica, vol. 157, no. 1, pp. 154-214 . https://doi.org/10.1112/S0010437X20007642
Compositio Mathematica

In this paper we prove a categorification of the Grothendieck-Riemann-Roch theorem. Our result implies in particular a Grothendieck-Riemann-Roch theorem for To\"en and Vezzosi's secondary Chern character. As a main application, we establish a compari

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::57c32f66081c7120f218282fd89bf72b
http://hdl.handle.net/20.500.11767/128270