Related papers: On the hyperreal dual Steenrod algebra

We describe a deformation of the $\infty$-category of Borel $G$-spectra for a finite group $G$. This provides a new presentation of the $a$-complete real Artin--Tate motivic stable homotopy category when $G=C_2$ and gives a new…

Let $A$ be an abelian compact Lie group and let $E$ be an oriented $A$-spectrum. We compute the $E$-homology of tom Dieck's homotopical $A$-equivariant complex bordism spectrum $MU_A$ in two ways, correcting an error in Cole-Greenlees-Kriz…

We consider $G=Q_8,SD_{16},G_{24},$ and $G_{48}$ as finite subgroups of the Morava stabilizer group which acts on the height $2$ Morava $E$-theory $\mathbf{E}_2$ at the prime $2$. We completely compute the $G$-homotopy fixed point spectral…

We compute the additive structure of the $\mathrm{RO}(C_n)$-graded Bredon equivariant cohomology of the equivariant classifying space $B_{C_n}\mathrm{SU}(2)$, for any $n$ that is either prime or a product of distinct odd primes, and we also…

Let $A$ be a cocommutative finite dimensional Hopf algebra over the field with two elements, satisfying some mild hypothesis. We set up a descent spectral sequence which computes the Picard group of the stable category of modules over $A$.…

For the cyclic group $C_2$ we give a complete description of the derived category of perfect complexes of modules over the constant Mackey ring $\underline{\mathbb{Z}/\ell}$, for $\ell$ a prime. This is fairly simple for $\ell$ odd, but for…

Let $H$ be a Hopf algebra. We consider $H$-equivariant modules over a Hopf module category $\mathcal C$ as modules over the smash extension $\mathcal C\# H$. We construct Grothendieck spectral sequences for the cohomologies as well as the…

In this paper, we investigate equivariant quotients of the Real bordism spectrum's multiplicative norm $MU^{((C_{2^n}))}$ by permutation summands. These quotients are of interest because of their close relationship with higher real…

For any $E_\infty$ ring spectrum $E$, we show that there is an algebra $\mathrm{Pow}(E)$ of stable power operations that acts naturally on the underlying spectrum of any $E$-algebra. Further, we show that there are maps of rings $E \to…

We compute the slices and slice spectral sequence of integral suspensions of the equivariant Eilenberg-Mac Lane spectra $H\underline{\mathbb{Z}}$ for the group of equivariance $Q_8$. Along the way, we compute the Mackey functors…

The second cohomology group (SCG) of the Jordan superalgebra $\mathcal{D}_{t}$, $t\neq 0$, is calculated by using the coefficients which appear in the regular superbimodule $\mathrm{Reg}\mathcal{D}_t$. Contrary to the case of algebras, this…

We construct a $C_2$-equivariant spectral sequence for RO$(C_2)$-graded homotopy groups. The construction is by using the motivic effective slice filtration and the $C_2$-equivariant Betti realization. We apply the spectral sequence to…

We construct a cycle in higher Hochschild homology associated to the 2-dimensional torus which represents 2-holonomy of a non-abelian gerbe in the same way the ordinary holonomy of a principal G-bundle gives rise to a cycle in ordinary…

We show that the algebra of commuting Hamiltonians of the homogeneous XXX Heisenberg model has simple spectrum on the subspace of singular vectors of the tensor product of two-dimensional $gl_2$-modules. As a byproduct we show that there…

Let $G$ be a finite group. For a based $G$-space $X$ and a Mackey functor $M$, a topological Mackey functor $X\widetilde\otimes M$ is constructed, which will be called the stable equivariant abelianization of $X$ with coefficients in $M$.…

Over the real numbers with $\Z/2-$coefficients, we compute the $C_2$-equivariant Borel motivic cohomology ring, the Bredon motivic cohomology groups and prove that the Bredon motivic cohomology ring of the real numbers is a proper subring…

In his seminal work on localisation of spectra, Ravenel initiated the study of Bousfield classes of spectra related to the chromatic perspective. In particular he showed that there were infinitely many distinct Bousfield classes between…

We give an explicit formula for the $RO(C_{2^n})$-graded homotopy of $H\underline{\mathbb{F}_2}$.

We compute the Balmer spectrum of a certain tensor triangulated category of comodules over the mod 2 dual Steenrod algebra. This computation effectively classifies the thick subcategories, resolving a conjecture of Palmieri.

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of…