nLab Marc Hoyois

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Selected writings

On Grothendieck's six operations in equivariant motivic homotopy theory:

• Marc Hoyois, The six operations in equivariant motivic homotopy theory, Adv. Math. 305 (2017) 197-279 [arXiv:1509.02145, doi:10.1016/j.aim.2016.09.031]

On representability in motivic homotopy theory:

and representability:

• Aravind Asok, Marc Hoyois, Matthias Wendt, Affine representability results in $\mathbb{A}^1$-homotopy theory I: Vector bundles, Duke Math. J. 166 10 (2017) 1923-1953 [arXiv:1506.07093, doi:10.1215/00127094-0000014X]

• Aravind Asok, Marc Hoyois, Matthias Wendt, Affine representability results in $\mathbb{A} ^1$-homotopy theory II: Principal bundles and homogeneous spaces, Geom. Topol. 22 (2018) 1181-1225 [arXiv:1507.08020, doi:10.2140/gt.2018.22.1181]

On Joyal $\infty$-loci:

• Marc Hoyois, Topoi of parametrized objects, Theory and Applications of Categories, 34 9 (2019) 243-248 [arXiv:1611.02267, tac:34-09]

On the Quillen plus construction in (∞,1)-category theory:

• Marc Hoyois, On Quillen’s plus construction, 2019 (pdf)

On a construction of algebraic cobordism as a non-$\mathbb{A}^1$-invariant cohomology theory on derived schemes, and the resulting Conner-Floyd isomorphism:

• Toni Annala, Marc Hoyois, Ryomei Iwasa, Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory [arXiv:2303.02051]

Related entries

• motivic homotopy theory
• étale homotopy

category: people