Related papers: $\mathbb{E}_\infty$ automorphisms of motivic Morav…

We study semistable symmetric spectra based on quite general monoidal model categories, including motivic examples. In particular, we establish a generalization of Schwede's list of equivalent characterizations of semistability in the case…

For cohomology theories closely related to Morava E-theory, we provide an algebro-geometric interpretation of the cohomology of groups that arise as centralizers of tuples of commuting elements inside of symmetric groups. The interpretation…

Let $X$ be a Noetherian separated scheme of finite Krull dimension. We show that the layers of the slice filtration in the motivic stable homotopy category $\stablehomotopy$ are strict modules over Voevodsky's algebraic cobordism spectrum.…

The question of existence of outer automorphisms of a simple algebraic group $G$ arises naturally both when working with the Galois cohomology of $G$ and as an example of the algebro-geometric problem of determining which connected…

By a Liouville structure on a symplectic manifold $(M, \omega)$ we mean a choice of symplectic potential: that is, a choice of one-form $\theta$ on $M$ such that ${\rm d} \theta = \omega$. We determine precisely all the automorphisms of a…

In this paper, we study profinite descent theory for Picard groups in $K(n)$-local homotopy theory through their inverse limit topology. Building upon Burklund's result on the multiplicative structures of generalized Moore spectra, we prove…

This article investigates a few questions about orbits of local automorphisms in manifolds endowed with rigid geometric structures. We give sufficient conditions for local homogeneity in a broad class of such structures, namely Cartan…

We develop a theory of motivic spectra in a broad generality; in particular $\mathbb{A}^1$-homotopy invariance is not assumed. As an application, we prove that $K$-theory of schemes is a universal Zariski sheaf of spectra which is equipped…

This is a survey paper on cohomology theories for $A_\infty$ and $E_\infty$ ring spectra. Different constructions and main properties of topological Andr\'e-Quillen cohomology and of topological derivations are described. We give sample…

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…

We look at the automorphisms of Thompson type groups of piecewise linear homeomorphisms of the real line or circle that use slopes that are integral powers of a fixed integer n with n>2. We show that large numbers of "exotic" automorphisms…

We compute the co-multiplication of the algebraic Morava K-theory for split orthogonal groups. This allows us to compute the decomposition of the Morava motives of generic maximal orthogonal Grassmannians and to compute a Morava K-theory…

We establish natural splittings for the values of global Mackey functors at orthogonal, unitary and symplectic groups. In particular, the restriction homomorphisms between the orthogonal, unitary and symplectic groups of adjacent dimensions…

Over the past century, cohomology operations have played a crucial role in homotopy theory and its applications. A powerful framework for constructing such operations is the theory of commutative algebras in spectra. In this article, we…

We analyze K3 surfaces admitting an elliptic fibration $E$ and a finite group $G$ of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration $E/G$ comparing its properties to the ones of…

Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real $K$-theory spectra of Hopkins and Miller at height $n=p-1$, for $p$ an odd prime. More generally, we determine the…

We study the automorphism groups of countable homogeneous directed graphs (and some additional homogeneous structures) from the point of view of topological dynamics. We determine precisely which of these automorphism groups are amenable…

We establish a formal framework for Rognes's homotopical Galois theory and adapt it to the context of motivic spaces and spectra. We discuss examples of Galois extensions between Eilenberg-MacLane motivic spectra and between the Hermitian…

We prove potential automorphy results for a single Galois representation $G_F \rightarrow GL_n(\overline{\mathbb{Q}}_l)$ where $F$ is a CM number field. The strategy is to use the $p,q$ switch trick and modify the Dwork motives employed in…

Let n \geq 1 and let p be any prime. Also, let E_n be the Lubin-Tate spectrum, G_n the extended Morava stabilizer group, and K(n) the nth Morava K-theory spectrum. Then work of Devinatz and Hopkins and some results due to Behrens and the…