Related papers: Tannaka duality revisited
We show that the $\mathbb{Z}/2$-equivariant Morava K-theories with reality (as defined by Hu) are self-dual with respect to equivariant Anderson duality. In particular, there is a universal coefficients exact sequence in Morava K-theory…
We establish a Galois connection between sub-monads of an augmented monad and sub-functors of the forgetful functor from its Eilenberg-Moore category. This connection is given in terms of invariants and stabilizers defined through universal…
We show that certain isomorphisms of (twisted) KR-groups that underlie T-dualities of torus orientifold string theories have purely algebraic analogues in terms of algebraic K-theory of real varieties and equivalences of derived categories…
Given a smooth projective toric variety $X_\Sigma$ of complex dimension $n$, Fang-Liu-Treumann-Zaslow \cite{FLTZ} showed that there is a quasi-embedding of the differential graded (dg) derived category of coherent sheaves $Coh(X_\Sigma)$…
We prove that the strange duality conjecture of Beauville-Donagi-Tu holds for all curves. We establish first a more extended rank-level duality, interesting in its own right, from which the standard rank-level duality follows by…
Holm (H. Holm, Modules with cosupport and injective functors, Algebr. Represent. Theor., 13 (2010), 543-560) considers categories of right modules dual to those with support in a set of finitely presented modules. We extend some of his…
A $K$-equivalent map between two smooth projective varieties is called simple if the map is resolved in both sides by single smooth blow-ups. In this paper, we will provide a structure theorem of simple $K$-equivalent maps, which reduces…
We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a skew-commutativity relation…
We study certain Schur functors which preserve singularity categories of rings and we apply them to study the singularity category of triangular matrix rings. In particular, combining these results with Buchweitz-Happel's theorem, we can…
This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…
In this paper, we establish a theorem that proves a condition when an inclusion morphism between simplicial sets becomes a weak homotopy equivalence. Additionally, we present two applications of this result. The first application…
We give sharp criteria for when a reductive group scheme satisfies Tannakian reconstruction. When the base scheme is Noetherian, we explicitly identify its Tannaka group scheme.
Frobenius monoidal functors preserve duals. We show that conversely, (co)monoidal functors between autonomous categories which preserve duals are Frobenius monoidal. We apply this result to linearly distributive functors between autonomous…
We study the representation theory of the Lie superalgebra $\mathfrak{gl}(1|1)$, constructing two spectral sequences which eventually annihilate precisely the superdimension zero indecomposable modules in the finite-dimensional category.…
Given an algebraic stack $X$, one may compare the derived category of quasi-coherent sheaves on $X$ with the category of dg-modules over the dg-ring of functions on $X$. We study the analogous question in stable homotopy theory, for derived…
Orlov's famous representability theorem asserts that any fully faithful functor between the derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. This result has been extended by Lunts and Orlov…
We describe new structure on the Goodwillie derivatives of a functor, and we show how the full Taylor tower of the functor can be recovered from this structure. This new structure takes the form of a coalgebra over a certain comonad which…
We study the intersection theory of complex Lagrangian subvarieties inside holomorphic symplectic manifolds. In particular, we study their behaviour under Mukai flops and give a rigorous proof of the Pl\"ucker type formula for Legendre dual…
We construct a monoidal version of Lurie's un/straightening equivalence. In more detail, for any symmetric monoidal $\infty$-category $\mathbf C$, we endow the $\infty$-category of coCartesian fibrations over $\mathbf C$ with a (naturally…
In a series of papers, we have shown that from the \repn theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we introduce the Tannaka…