Related papers: Invertible objects in Franke's comodule categories

We apply the theory of large-scale geometry of Polish groups to groups of absolutely continuous homeomorphisms. Let $M$ be either the compact interval or circle. We prove that the Polish group $\operatorname{AC}_+(M)$ of…

Cohen proved that the infinite variable polynomial ring $R=k[x_1,x_2,\ldots]$ is noetherian with respect to the action of the infinite symmetric group $\mathfrak{S}$. The first two authors began a program to understand the…

For each integer n\ge 2, we construct an irreducible, smooth, complex projective variety M of dimension n, whose fundamental group has infinitely generated homology in degree n+1 and whose universal cover is a Stein manifold, homotopy…

There are many previous studies on the Hopf algebra $K(n)_*(K(n))$, the stable cooperations of $n$th Morava $K$-theory at an odd prime. Whereas the main part of $K(n)_*(K(n))$ corepresents the group-valued functor consisting of strict…

Let $G$ be a finite group of order $n$ and let $M$ be a $G$-module. We construct groups $H_*^\varkappa(G,M)$ for which $H_k^\varkappa (G,M^{tw}) \cong H^{n-k-1}_\lambda(G,M),$ where $M^{tw}$ is a twisting of a $G$-module $M$ defined in…

We compute the algebraic Picard group of the category of $K(n)$-local spectra, for all heights $n$ and all primes $p$. In particular, we show that it is always finitely generated over $\mathbb{Z}_p$ and, whenever $n \geq 2$, is of rank $2$,…

There is a natural action of a kind of Hecke algebra $\mathcal{H}_n$ on the $n$th Morava $E$-theory of spaces. We construct Hecke operators in an amalgamated cohomology theory of the $n$th and the $(n+1)$st Morava $E$-theories. These…

The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for…

Given an irreducible non-spherical non-affine (possibly non-proper) building $X$, we give sufficient conditions for a group $G < \Aut(X)$ to admit an infinite-dimensional space of non-trivial quasi-morphisms. The result applies to all…

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 $A$.…

This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their…

A recent theorem by T. Barthel, M. Hausmann, N. Naumann, T. Nikolaus, J. Noel, and N. Stapleton says that if A is a finite abelian p-group of rank r, then any finite A-space X which is acyclic in the nth Morava K-theory with n at least r…

Let $G$ be a split connected reductive group over the ring of integers of a finite unramified extension $K$ of $\mathbf{Q}_p$. Under a standard assumption on the Coxeter number of $G$, we compute the cohomology algebra of $G(\mathcal{O}_K)$…

It has been conjectured that the classical dynamics of M theory is equivalent to a null geodesic motion in the infinite-dimensional coset space E10/K(E10) where K(E10) is the maximal compact subgroup of the hyperbolic Kac-Moody group E10.…

Let X be a smooth projective variety of dimension n. If $p+q=n+1$ then Bloch has defined a ${\bf G}_m$-biextension E over the product of the Chow groups $CH^p_0(X)$ and $CH^q_0(X)$ of homologically trivial cycles. We prove that E is the…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

Let $X$ be a smooth complex quasi-projective variety that is special in the sense of Campana. We prove that the monodromy group of any complex local system on $X$ is virtually nilpotent of class at most $2$. This result sharply refines a…

We show that instanton bundles of rank $r\le 2n-1$, defined as the cohomology of certain linear monads, on an $n$-dimensional projective variety with cyclic Picard group are semistable in the sense of Mumford-Takemoto. Furthermore, we show…

We investigate Hopf algebroids in the category of $L$-complete modules over a commutative Noetherian regular complete local ring. The main examples are provided by the Hopf algebroids associated to Lubin-Tate spectra in the K(n)-local…

We prove that a finite braided tensor category A is invertible in the Morita 4-category BrTens of braided tensor categories if, and only if, it is non-degenerate. This includes the case of semisimple modular tensor categories, but also…