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Let $X$ be a (-1)-shifted symplectic derived Deligne--Mumford stack. In this paper we introduce the Darboux stack of $X$, parametrizing local presentations of $X$ as a derived critical locus of a function $f$ on a smooth formal scheme $U$. Local inva
Externí odkaz:
http://arxiv.org/abs/2407.08471
Autor:
Robalo, Marco
In this short note we record the fact that the set of multiplicative HKR natural equivalences defined simultaneously for all derived schemes, functorialy splitting the HKR-filtration and rendering the circle action compatible with the de Rham differe
Externí odkaz:
http://arxiv.org/abs/2310.05859
Publikováno v:
Geom. Topol. 26 (2022) 777-874
In this work we study the failure of the HKR theorem over rings of positive and mixed characteristic. For this we construct a filtered circle interpolating between the usual topological circle and a formal version of it. By mapping to schemes we prod
Externí odkaz:
http://arxiv.org/abs/1906.00118
Autor:
Mann, Etienne, Robalo, Marco
In this survey we add two new results that are not in our paper [MR15]. Using the idea of brane actions discovered by Toen, we construct a lax associative action of the operad of stable curves of genus zero on a smooth variety X seen as an object in
Externí odkaz:
http://arxiv.org/abs/1803.09476
Autor:
Robalo, Marco, Schapira, Pierre
Microlocal sheaf theory of \cite{KS90} makes an essential use of an extension lemma for sheaves due to Kashiwara, and this lemma is based on a criterion of the same author giving conditions in order that a functor defined in $\mathbb{R}$ with values
Externí odkaz:
http://arxiv.org/abs/1611.06789
Autor:
Mann, Etienne, Robalo, Marco
Publikováno v:
Geom. Topol. 22 (2018) 1759-1836
Let X be a smooth projective variety. Using the idea of brane actions discovered by To\"en, we construct a lax associative action of the operad of stable curves of genus zero on the variety X seen as an object in correspondences in derived stacks. Th
Externí odkaz:
http://arxiv.org/abs/1505.02964
Autor:
Robalo, Marco
We continue the work initiated in arXiv:1206.3645, where we introduced a new stable symmetric monoidal $(\infty,1)$-category $SH_{nc}$ encoding a motivic stable homotopy theory for the noncommutative spaces of Kontsevich and obtained a canonical mono
Externí odkaz:
http://arxiv.org/abs/1306.3795
Autor:
Robalo, Marco
Let $\V$ be a symmetric monoidal model category and let $X$ be an object in $\V$. From this we can construct a new symmetric monoidal model category $Sp^{\Sigma}(\V,X)$ of symmetric spectra objects in $\V$ with respect to $X$, together with a left Qu
Externí odkaz:
http://arxiv.org/abs/1206.3645
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