Related papers: Desuspensions of S^1 /\ P^1_Q-{0,1,infty}

We give a tool for understanding simplicial desuspension in A1-algebraic topology: we show that $X \to \Omega (S^1 \wedge X)\to \Omega (S^1 \wedge X \wedge X)$ is a fiber sequence up to homotopy in 2-localized A1-algebraic topology for $X =…

The aim of this paper is to study cohomogeneity one isometric linear actions on the $p+q$-dimensional pseudo-Euclidean space $\mathbb{R}^{p,q}$. It is proved that the natural isometric action of the nilpotent factor of an Iwasawa…

Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H^1(G,…

Let K be a complete discrete valuation field of mixed characteristic (0,p) with perfect residue field. Let (\pi_n)_{n\ge 0} be a system of p-power roots of a uniformizer \pi=\pi_0 of K with \pi^p_{n+1}=\pi_n, and define G_s (resp.\…

We consider the SQG equation without dissipation on the half-plane with Dirichlet boundary condition, and prove local wellposedness in the spaces $W^{3,p}$ and $C^{2,\beta}$ for any $1<p<\infty$ and $0<\beta<1$. We complement this…

This paper establishes restrictions on the possible Galois actions on the pro-l-unipotent fundamental group of a smooth variety X of good reduction over a local field K. In particular, if X is proper and l is not equal to the residue…

We prove that any semi-simple representation of the Galois group of a number field coming from geometry appears as a subquotient of the ring of regular functions on the pro-algebraic completion of the fundamental group of the projective…

We study the simplicial {\ell} q,p cohomology of Carnot groups G. We show vanishing and non-vanishing results depending of the range of the (p, q) gap with respect to the weight gaps in the Lie algebra cohomology of G.

We study the action of the Galois group on the pro-l-completion of the fundamental group of P^1 - {0, infinity and N-th roots of unity}. We describe the Lie algebra of the image of the Galois action and relate with the geometry of the…

Let $K$ be a finite extension of $\mathbb{Q}_p$, and choose a uniformizer $\pi\in K$, and put $K_\infty:=K(\sqrt[p^\infty]{\pi})$. We introduce a new technique using restriction to $\Gal(\ol K/K_\infty)$ to study flat deformation rings. We…

We define a derived version of Mazur's Galois deformation ring. It is a pro-simplicial ring $\mathcal{R}$ classifying deformations of a fixed Galois representation to simplicial coefficient rings; its zeroth homotopy group $\pi_0…

We prove in this paper an uniform surjectivity result for Galois representations associated with non-CM $\mathbb{Q}$-curves over imaginary quadratic fields, using various tools for the proof, such as Mazur's method, isogeny theorems,…

Motivated by a recent extension of the zero-one law by Kolaitis and Kopparty, we study the distribution of the number of copies of a fixed disconnected graph in the random graph $G(n,p)$. We use an idea of graph decompositions to give a…

The relationship between the exactness of a first order differential calculus on a comodule algebra $P$ and the Galois property of $P$ is investigated.

We prove an $l^p$ decoupling inequality for hypersurfaces with nonzero Gaussian curvature and use it to derive a corresponding $l^p$ decoupling for curves not contained in a hyperplane. This extends our earlier work from [2]

Generalized \'etale homotopy pro-groups $\pi_1^{\ets}(\mc{C}, x)$ associated to pointed connected small Grothendieck sites $(\mc{C}, x)$ are defined and their relationship to Galois theory and the theory of pointed torsors for discrete…

We show the classical $\pi_1$-action on the $n$-th homotopy group can fail to be continuous for any $n$ when the homotopy groups are equipped with the natural quotient topology. In particular, we prove the action…

Let $M$ be a smooth compact surface, orientable or not, with boundary or without it, $P$ either the real line $R^1$ or the circle $S^1$, and $Diff(M)$ the group of diffeomorphisms of $M$ acting on $C^{\infty}(M,P)$ by the rule $h\cdot…

Given a $G$-Galois branched cover of the projective line over a number field $K$, we study whether there exists a closed point of $\mathbb{P}^1_K$ with a connected fiber such that the $G$-Galois field extension induced by specialization…

We prove that the $L^1$ norm on the linear span of functions on $\T^\N$ dependent on $m$ variables and analytic and mean zero in each of them can be expressed as an interpolation sum of…