Related papers: Rigidity in etale motivic stable homotopy theory

We investigate a new case of rigidity in stable homotopy theory which is the rigidity of the $K(1)$-local stable homotopy category $\mathrm{Ho}(L_{K(1)}\mathrm{Sp})$ at $p=2$. In other words, we show that recovering higher homotopy…

In their construction of the topological index for flat vector bundles, Atiyah, Patodi and Singer associate to each flat vector bundle a particular $\mathbb{C/Z}$-$K$-theory class. This assignment determines a map, up to weak homotopy, from…

Let A_E be the canonical AF subalgebra of a graph C*-algebra C*(E) associated with a locally finite directed graph E. For Brown-Voiculescu's topological entropy ht(\Phi_E) of the canonical completely positive map \Phi_E on C*(E),…

We continue the work initiated in arXiv:1206.3645, where we introduced a new stable symmetric monoidal $(\infty,1)$-category $SH_{nc}$ encoding a motivic stable homotopy theory for the noncommutative spaces of Kontsevich and obtained a…

We show that the classifying space of the flow category of a \emph{tame} Morse function on a smooth, closed manifold $M$ recovers the homotopy type of $M$, thereby addressing a claim in a preprint of Cohen--Jones--Segal. The tameness…

If a finite group $G$ is isomorphic to a subgroup of $SO(3)$, then $G$ has the D2-property. Let $X$ be a finite complex satisfying Wall's D2-conditions. If $\pi_1(X)=G$ is finite, and $\chi(X) \geq 1-Def(G)$, then $X \vee S^2$ is simple…

We extend McCarthy's stabilization construction to exact $\infty$-categories. This is achieved by constructing, for any functor from exact $\infty$-categories to a fixed stable $\infty$-category $\mathcal{A}$, a coherent chain complex in…

We calculate the motivic stable homotopy groups of the two-complete sphere spectrum after inverting multiplication by the Hopf map eta over fields of cohomological dimension at most 2 with characteristic different from 2 (this includes the…

We prove that the category $\textbf{G-Cat}$ of small categories with $G$-action forms a model of unstable $G$-global homotopy theory for every discrete group $G$, generalizing Schwede's global model structure on $\textbf{Cat}$. As a…

We establish a purely geometric form of the concentration theorem (also called localization theorem) for actions of a linearly reductive group $G$ on an affine scheme $X$ over an affine base scheme $S$. It asserts the existence of a…

For (X,L) a polarized toric variety and G a torus of automorphisms of (X,L), denote by Y the GIT quotient X/G. We define a family of fully faithful functors from the category of torus equivariant reflexive sheaves on Y to the category of…

We prove that a Hamiltonian $p\in C^\infty(T^*{\bf R}^n)$ is locally integrable near a non-degenerate critical point $\rho_0$ of the energy, provided that the fundamental matrix at $\rho_0$ has no purely imaginary eigenvalues. This is done…

We set up a real entropy function $h_\Bbb{R}$ on the space $\mathcal{M}'_d$ of M\"obius conjugacy classes of real rational maps of degree $d$ by assigning to each class the real entropy of a representative $f\in\Bbb{R}(z)$; namely, the…

Let $p \geq 5$ be a prime number and let $G = SL_2(\mathbb{Q}_p)$. Let $\Xi$ = Spec$(Z)$ denote the spectrum of the centre $Z$ of the pro-$p$ Iwahori Hecke algebra of $G$ with coefficients in a field $k$ of characteristic $p$. Let…

In this paper we show that it is possible to define a topology on the category of formal schemes over a ring of $p$-adic integers such that the left adjoint of the Greenberg Transform is a site cocontinuous functor when we equip the…

We study differential graded operads and $p$-adic stable homotopy theory. We first construct a new class of differential graded operads, which we call the stable operads. These operads are, in a particular sense, stabilizations of…

Let $k$ be an algebraically closed field of characteristic $0$ or $p>2$. Let $\mathcal{G}$ be an affine supergroup scheme over $k$. We classify the indecomposable exact module categories over the tensor category ${\rm sCoh}_{\rm…

Let $G$ denote a possibly discrete topological group admitting an open subgroup $I$ which is pro-$p$. If $H$ denotes the corresponding Hecke algebra over a field $k$ of characteristic $p$ then we study the adjunction between $H$-modules and…

Let $B$ be a C$^*$-algebra and $X$ a C$^*$ Hilbert $B$-module. If $p\in B$ is a projection, denote by $S_p =\{x\in X : < x,x> =p\}$, the $p$-sphere of $X$. For $\phi$ a state of $B$ with support $p$ in $B$ and $x\in S_p$, consider the state…

We prove that every finite symmetric integral tensor category $\mathcal{C}$ with the Chevalley property over an algebraically closed field $k$ of characteristic $p>2$ admits a symmetric fiber functor to $\text{sVec}$. This proves Ostrik's…