Related papers: Equivariant Universal Coefficient and Kunneth Spec…

Arone and Lesh constructed and studied spectrum level filtrations that interpolate between connective (topological or algebraic) K-theory and the Eilenberg-MacLane spectrum for the integers. In this paper we consider (global) equivariant…

We classify all tilting and cotilting classes over commutative noetherian rings in terms of descending sequences of specialization closed subsets of the Zariski spectrum. Consequently, all resolving subcategories of finitely generated…

In this paper, we investigate the properties of the category of equivariant diagram spectra indexed on the category W_G of based G-spaces homeomorphic to finite G-CW-complexes for a compact Lie group G. Using the machinery of Mandell, May,…

In this paper we develop the definition of a global orthogonal spectrum and its unitary version. It relates $G-$equivariant spectra by equivariant weak equivalence in a coherent way. This category of global spectra has a model structure…

We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line $\mathbf{S}[t]$ as a functor defined on the $\infty$-category of cyclotomic spectra with values in the $\infty$-category of spectra…

Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic…

We compute the $RO(\mathcal{K})$-graded coefficients of the equivariant Eilenberg-Mac Lane spectrum associated to various Hill-Hopkins-Ravenel norms of the constant-$\mathbb{F}_2$ Mackey functor, where $\mathcal{K}$ is the Klein-four group.…

In this paper we construct orthogonal $G-$spectra up to a weak equivalence for the quasi-theory $QE_{n, G}^*(-)$ corresponding to certain cohomology theories $E$. The construction of the orthogonal $G-$spectrum for quasi-elliptic cohomology…

We introduce the notion of $\mathrm{R}$-Eulerian sequences for any $\mathcal{N}_\infty$-ring spectrum $\mathrm{R}$ of finite orientation order. We prove that each $\mathrm{R}$-Eulerian sequence determines a stable $\mathrm{R}$-cohomology…

Let $R$ be a local ring of characteristic $p>0$ which is $F$-finite and has perfect residue field. We compute the generalized Hilbert-Kunz invariant for certain modules over several classes of rings: hypersurfaces of finite representation…

Given a finite-dimensional complex Lie algebra g equipped with a nondegenerate, symmetric, invariant bilinear form B, let V_k(g,B) denote the universal affine vertex algebra associated to g and B at level k. For any reductive group G of…

Let A be a dg category, F:A->A a dg functor inducing an equivalence of categories in degree-zero cohomology, and A/F the associated dg orbit category. For every A1-homotopy invariant (e.g. homotopy K-theory, K-theory with coefficients,…

Let G be a reductive linear algebraic group over a field k. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. Invariant theory tells that the ring of invariants A^G=H^0(G,A) is…

Given a unital action $\theta $ of an inverse monoid $S$ on an algebra $A$ over a filed $K$ we produce (co)homology spectral sequences which converge to the Hochschild (co)homology of the crossed product $A\rtimes_\theta S$ with values in a…

We consider infinite tensor product actions of $G = \mathbb{Z}/p\mathbb{Z}$ on the UHF-algebra $D = \text{End}(V)^{\otimes \infty}$ for a finite-dimensional unitary $G$-representation $V$ and determine the equivariant homotopy type of the…

If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point spectrum Z^{hK} is Map_*(EK_+, Z)^K, the fixed points of a familiar expression. Similarly, if G is a profinite group and X is a discrete G-spectrum, then X^{hG}…

We introduce a scissors congruence $K$-theory spectrum which lifts the equivariant scissors congruence groups for compact $G$-manifolds with boundary, and we show that on $\pi_0$ this is the source of a spectrum level lift of the Burnside…

A central question in equivariant algebraic K-theory asks whether there exists an equivariant K-theory machine from genuine symmetric monoidal G-categories to orthogonal G-spectra that preserves equivariant algebraic structures. We answer…

We classify thick subcategories of the $\infty$-categories of perfect modules over ring spectra which arise as functions on even periodic derived stacks satisfying affineness and regularity conditions. For example, we show that the thick…

We initiate the study of deformation theory in the context of derived and higher log geometry. After reconceptualizing the "exactification"-procedures in ordinary log geometry in terms of Quillen's approach to the cotangent complex, we…