相关论文: Equivariant localizing invariants of simple variet…

We use Drinfeld style generators and relations to define an algebra $\mathfrak{U}_n$ which is a ``$q=0$'' version of the affine quantum group of $\mathfrak{gl}_n.$ We then use the convolution product on the equivariant $K$-theory of…

Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner, the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterized in…

We study the equivariant K-group of the affine flag manifold with respect to the Borel group action. We prove that the structure sheaf of the (infinite-dimensional) Schubert variety in the K-group is represented by a unique polynomial,…

In Part II, we saw how genus-0 permutation-equivariant quantum K-theory of a manifold with isolated fixed points of a torus action can be reduced via fixed point localization to permutation-equivariant quantum K-theory of the point. In Part…

This submission is a PhD dissertation. It constitutes the summary of the author's work concerning the relations between cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed point schemes. It includes the…

A natural higher K-theoretic analogue of the triviality of vector bundles on affine toric varieties is the conjecture on nilpotence of the multiplicative action of the natural numbers on the K-theory of these varieties. This includes both…

We define the motivic filtrations on real topological Hochschild homology and its companions. In particular, we prove that real topological cyclic homology admits a natural complete filtration whose graded pieces are equivariant suspensions…

We prove an analogue of the Gabriel--Quillen embedding theorem for exact $\infty$-categories, giving rise to a presentable version of Klemenc's stable envelope of an exact $\infty$-category. Moreover, we construct a symmetric monoidal…

We provide a new construction of the topological cyclic homology $TC(C)$ of any spectrally-enriched $\infty$-category $C$, which affords a precise algebro-geometric interpretation of the cyclotomic trace map $K(X) \to TC(X)$ from algebraic…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

In this paper we study a model structure on a category of schemes with a group action and the resulting unstable and stable equivariant motivic homotopy theories. The new model structure introduced here samples a comparison to the one by…

We do three things in this paper: (1) study the analog of localization sequences (in the sense of algebraic $K$-theory of stable $\infty$-categories) for additive $\infty$-categories, (2) define the notion of nilpotent extensions for…

We construct a new family of knot concordance invariants $\theta^{(q)}(K)$, where $q$ is a prime number. Our invariants are obtained from the equivariant Seiberg-Witten-Floer cohomology, constructed by the author and Hekmati, applied to the…

For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…

In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…

We prove that the Bowen-Franks group classifies the Leavitt path algebras of purely infinite simple finite graphs over a regular supercoherent commutative ring with involution where $2$ is invertible, equipped with their standard…

We realize a graded variant $K_0(Var_k^{dim})$ of the Grothendieck ring of varieties as a quadratic extension of the subring $K_0(Var_k^{sp})$ spanned by classes of smooth and proper varieties. As such, there exists a natural involution…

We provide a unified geometric realization of the classical deformation complexes. We construct GL-equivariant bilinear incidence varieties whose diagonal slices recover the varieties of associative, commutative, Leibniz, and Lie algebra…

We prove a version of Quillen's stratification theorem in equivariant homotopy theory for a finite group $G$, generalizing the classical theorem in two directions. Firstly, we work with arbitrary commutative equivariant ring spectra as…

Let $\sigma$ be a simple involution of an algebraic semisimple group $G$ and let $H$ be the subgroup of $G$ of points fixed by $\sigma$. If the restricted root system is of type $A$, $C$ or $BC$ and $G$ is simply connected or if the…