Related papers: Very Schwartz coidempotents and continuous spectru…
(This is an updated version; following an idea of Voevodsky, we have strengthened our results so all of them apply to one form of motivic homotopy theory). We give two general constructions for the passage from unstable to stable homotopy…
We survey some methods developed in a series of papers, for classifying localising subcategories of tensor triangulated categories. We illustrate these methods by proving a new theorem, providing such a classification in the case of the…
A stable $\infty$-category is $1$-semiadditive if the norms for all finite group actions are equivalences. In the presence of $1$-semiadditivity, Goodwillie calculus simplifies drastically. We introduce two variants of $1$-semiadditivity…
Our main observation is that the contravariant functor Spec on the category of commutative monoids is representable. We discuss a few consequences of this fact. In particular, we give an efficient way of calculating the Spec(M) of a…
We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for a large class of compact locally Riemannian homogeneous spaces, in particular all compact locally symmetric spaces. This…
Given a moduli problem posed using Geometric Invariant Theory, one can use Non-Reductive Geometric Invariant Theory to quotient unstable HKKN strata and construct 'moduli spaces of unstable objects', extending the usual moduli…
We consider contractive operators $T$ that are trace class perturbations of a unitary operator $U$. We prove that the dimension functions of the absolutely continuous spectrum of $T$, $T^*$ and of $U$ coincide. In particular, if $U$ has a…
We construct a compactification $M^{\mu ss}$ of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective…
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with…
In this paper, we construct incomplete versions of the equivariant stable category; i.e., equivariant stabilization of the category of $G$-spaces with respect to incomplete systems of transfers encoded by an $N_\infty$ operad $\mathcal{O}$.…
In the work it is shown that the space of idempotent probability measures with compact supports is kappa-metrizable if the given Tychonoff space is kappa-metrizable. It is constructed a series of max-plus-convex subfunctors of the functor…
We study the stabilization of complex structure moduli in Type IIB flux compactifications by using recent general results about the form of the superpotential and K\"ahler potential near the boundaries of the moduli space. In this process…
We show the absolute continuity of the spectrum and determine the spectrum as a set for two classes of Hadamard manifolds and for specific domains and quotients of one of the classes.
It is proved that the category $\mathbb{EM}$ of extended multisets is dually equivalent to the category $\mathbb{CHMV}$ of compact Hausdorff MV-algebras with continuous homomorphisms, which is in turn equivalent to the category of complete…
This paper studies the foundations of the geometric fixed point functor in multiplicative equivariant stable homotopy theory. We introduce a new class of equivariant orthogonal spectra called generalized orbit desuspension spectra and…
An old theorem of Charney and Lee says that the classifying space of the category of stable nodal topological surfaces and isotopy classes of degenerations has the same rational homology as the Deligne-Mumford compactification. We give an…
We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with…
Bondarko's (strong) weight complex functor is a triangulated functor from Voevodsky's triangulated category of motives to the homotopy category of chain complexes of classical Chow motives. Its construction is valid for any dg enhanced…
Every small monoidal category with universal finite joins of central idempotents is monoidally equivalent to the category of global sections of a sheaf of local monoidal categories on a topological space. Every small stiff monoidal category…
We prove that the space of complex irreducible polynomials of degree $d$ in $n$ variables satisfies two forms of homological stability: first, its cohomology stabilizes as $d$ increases, and second, its compactly supported cohomology…