arXiv subjects

Sebastian Ørsted

Publications and source records attributed to Sebastian Ørsted.

4 recordsLinked to original sources

arXiv2026

The ring of $ω$-invariant symmetric functions in characteristic 2

We provide a simple presentation by generators and relations of the ring of $ω$-invariant symmetric functions over the field $\mathbb{F}_{2}$. Here, $ω$ denotes the standard involution on the ring of symmetric functions, interchanging the elementary symmetric functions with the complete homogeneous symmetric functions. Along the way, we prove several important properties of this involution in the specific setting of characteristic 2.

math.AC↗

arXiv2023

Equivariant sheaves on loop spaces

Let $X$ be an affine, smooth, and Noetherian scheme over $\mathbb{C}$ acted on by an affine algebraic group $G$. Applying the technique developed in Arkhipov and Ørsted (2018a, 2018b), we define a dg-model for the derived category of dg-modules over the dg-algebra of differential forms $Ω_X$ on $X$ equivariant with respect to the action of a derived group scheme $(G ,Ω_G )$. We compare the obtained dg-category with the one considered in Arkhipov and Kanstrup (2015) given by coherent sheaves on the derived Hamiltonian reduction of $T^* X$.

math.RT↗

arXiv2019

Homotopy (co)limits via homotopy (co)ends in general combinatorial model categories

We prove and explain several classical formulae for homotopy (co)limits in general (combinatorial) model categories which are not necessarily simplicially enriched. Importantly, we prove versions of the Bousfield-Kan formula and the fat totalization formula in this complete generality. We finish with a proof that homotopy-final functors preserve homotopy limits, again in complete generality.

math.CT↗

arXiv2019

Homotopy limits in the category of dg-categories in terms of $\mathrm{A}_{\infty}$-comodules

In this paper, we apply an explicit construction of a simplicial powering in dg-categories, due to Holstein (2016) and Arkhipov and Poliakova (2018), as well as our own results on homotopy ends (Arkhipov and Ørsted 2018), to obtain an explicit model for the homotopy limit of a cosimplicial system of dg-categories. We apply this to obtain a model for homotopy descent in terms of $\mathrm{A}_{\infty}$-comodules, proving a conjecture by Block, Holstein, and Wei (2017) in the process.

math.CT↗