Related papers: On the Pettis-Johnstone theorem for localic groups

We consider local-global principles for torsors under linear algebraic groups, over function fields of curves over complete discretely valued fields. The obstruction to such a principle is a version of the Tate-Shafarevich group; and for…

We prove that for any finite index subgroup of the mapping class group containing the Johnson subgroup, the profinite Birman exact sequence does not split in genus $g\ge 3$, extending prior results of Hain and the second author for $g\ge…

The descent method is one of the approaches to study the Brauer--Manin obstruction to the local--global principle and to weak approximation on varieties over number fields, by reducing the problem to ``descent varieties''. In recent lecture…

If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x…

This paper deals with the problem of conjugacy of Cartan subalgebras for affine Kac-Moody Lie algebras. Unlike the methods used by Peterson and Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of…

Let $K$ be an algebraically closed field of arbitrary characteristic and let $X$ be an irreducible projective variety over $K$. Let $G\subseteq\text{Bir}(X)$ be a bounded-degree subgroup. We prove that there exists an irreducible projective…

We generalize Breuil-Hellmann-Schraen's local model for the trianguline variety to certain points with non-regular Hodge-Tate weights. With the local models we are able to prove, under the Taylor-Wiles hypothesis, the existence of certain…

Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…

We give a new proof of the theorem of Birman-Powell that the Torelli subgroup of the mapping class group of a closed orientable surface of genus at least 3 is generated by simple homeomorphisms known as bounding pair maps. The key…

Thomason's \'{e}tale descent theorem for Bott periodic algebraic $K$-theory \cite{aktec} is generalized to any $MGL$ module over a regular Noetherian scheme of finite dimension. Over arbitrary Noetherian schemes of finite dimension, this…

Over any field of characteristic $0$, we prove that the homotopy exact sequence of algebraic fundamental groups for the universal curve with unordered marked points does not split. The same nonsplitting holds for the universal hyperelliptic…

Let $T$ be a locally finite tree all of whose vertices have valency at least $6$. We classify, up to isomorphism, the closed subgroups of $\mathrm{Aut}(T)$ acting $2$-transitively on the set of ends of $T$ and whose local action at each…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…

In this note we prove the classical decomposition theorems for certain subgroups of the automorphism group of the Bruhat-Tits tree associated to $\mathrm{PGL}_{2}(F)$, where $F$ is a local field. The results can be used to understand the…

We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the unramified Brauer group of G/H vanishes.

The purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory. Using the theorem we give another proof of the Bott residue formula for Chern numbers of bundles on smooth complete…

We show that every homomorphism from a one-dimensional Peano continuum to a planar Peano continuum is induced by a continuous map up to conjugation. We then prove that the topological structure of the space of points at which a planar Peano…

We prove that the conjugacy problem for the automorphism group of the random graph is Borel complete, and discuss the analogous problem for some other countably categorical structures.

For an algebraic torus defined over a local (or global) field $F$, a celebrated result of R.P. Langlands establishes a natural homomorphism from the group of continuous cohomology classes of the Weil group, valued in the dual torus, onto…