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Homotopy Sheaves on Generalised Spaces
We study the homotopy right Kan extension of homotopy sheaves on a category to its free cocompletion, i.e. to its category of presheaves. Any...
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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...
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The Singular Support of Sheaves Is γ-Coisotropic
We prove that the singular support of an element in the derived category of sheaves is γ -coisotropic, a notion defined in [Vit22]. We prove that this...
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Tensor triangular geometry of filtered objects and sheaves
We compute the Balmer spectra of compact objects of tensor triangulated categories whose objects are filtered or graded objects of (or sheaves valued...
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Simplicial Chern–Weil theory for coherent analytic sheaves, part II
In the previous part of this diptych, we defined the notion of an admissible simplicial connection , as well as explaining how H.I. Green constructed...
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The cube axiom and resolutions in homotopy theory
We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model...
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K-flatness and orthogonality in homotopy categories
K-flatness for unbounded complexes of modules over a ring R was introduced by Spaltenstein [27], as an analogue of the classical notion of flatness...
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Virasoro constraints for moduli of sheaves and vertex algebras
In enumerative geometry, Virasoro constraints were first conjectured in Gromov-Witten theory with many new recent developments in the sheaf theoretic...
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Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck
This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of...
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\({\mathfrak X}\) -Flat Pro-Quasi-Coherent Pro-Sheaves on \({\boldsymbol {\mathfrak Y}}\)
In this chapter, we consider a flat affine morphism of ind-schemes. In this context, we define the semiderived category of quasi-coherent torsion...
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The derived Brauer map via twisted sheaves
Let X be a quasicompact quasiseparated scheme. The collection of derived Azumaya algebras in the sense of Toën forms a group, which contains the...
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Stable homotopy groups of spheres: from dimension 0 to 90
Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, the second and the third author on the isomorphism between motivic...
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Surjectivity of the Étale Excision Map for Homotopy Invariant Framed Presheaves
AbstractThe categories of framed correspondences, framed presheaves, and framed sheaves were introduced by V. Voevodsky in his foundational “Notes...
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Perverse Sheaves and the Cohomology of Regular Hessenberg Varieties
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot action of...
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Nearby motivic sheaves of weighted equivariant functions
Let k be a field of characteristic zero and let X be an algebraic k -variety endowed with an action of the multiplicative algebraic monoid
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