Related papers: Finite torsors over strongly $F$-regular singulari…

We argue that M-theory compactified on an arbitrary genus-one fibration, that is, an elliptic fibration which need not have a section, always has an F-theory limit when the area of the genus-one fiber approaches zero. Such genus-one…

We prove that torsors under parahoric group schemes on the punctured spectrum of Fontaine's ring $A_{\mathrm{inf}}$, extend to the whole spectrum. Using descent we can extend a similar result for the ring $\mathfrak{S}$ of Kisin and Pappas…

We observe that any regular Lie groupoid G over an manifold M fits into an extension $K \to G \to E$ of a foliation groupoid E by a bundle of connected Lie groups K. If $\FF$ is the foliation on M given by the orbits of E and T is a…

We show that if f: X --> Y is a finite, separable morphism of smooth curves defined over a finite field F_q, where q is larger than an explicit constant depending only on the degree of f and the genus of X, then f maps X(F_q) surjectively…

For a fixed finite solvable group $G$ and number field $K$, we prove an upper bound for the number of $G$-extensions $L/K$ with restricted local behavior (at infinitely many places) and ${\rm inv}(L/K)<X$ for a general invariant $"{\rm…

We study the class of finite groups $G$ satisfying $\Phi (G/N)= \Phi(G)N/N$ for all normal subgroups $N$ of $G$. As a consequence of our main results we extend and amplify a theorem of Doerk concerning this class from the soluble universe…

We study the problem of $\mathfrak{m}$-adic stability of F-singularities, that is, whether the property that a quotient of a local ring $(R,\mathfrak{m})$ by a non-zero divisor $x \in \mathfrak{m}$ has good F-singularities is preserved in a…

In this paper we prove that if R is a left Noetherian and left regular ring such that all finitely generated projective left R-modules are stably free, then the same is true for the completion R[[x;\sigma,\delta]] of any Ore extension…

We prove that the torsion subgroup of the abelian fundamental group is finite for a regular geometrically integral projective variety over a local field. We also study the structure of $SK_1(X)$ for a regular projective variety $X$ over a…

We classify the allowed structures of the discrete 1-form gauge sector in six-dimensional supergravity theories realized as F-theory compactifications. This provides upper bounds on the 1-form gauge factors $\mathbb{Z}_m$ and in particular…

A generalized Baumslag-Solitar group (GBS group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains non-abelian free groups or is virtually…

Let $A$ be an abelian variety defined over a field $K.$ We study finite generation properties of the profinite group $\mathrm{Gal}(\Omega/K)$ and of certain closed normal subgroups thereof, where $\Omega$ is the torsion field of $A$ over…

Let $q$ be a unimodular quadratic form over a field $K$. Pfister's famous local--global principle asserts that $q$ represents a torsion class in the Witt group of $K$ if and only if it has signature $0$, and that in this case, the order of…

We provide new examples of groups without rational cross-sections (also called regular normal forms), using connections with bounded generation and rational orders on groups. Specifically, our examples are extensions of infinite torsion…

We prove that a saturated weakly branch group $G$ has the property $R_\infty$ (any automorphism $\phi:G\to G$ has infinite Reidemeister number) in each of the following cases: 1) any element of $Out(G)$ has finite order; 2) for any $\phi$…

We study the fundamental group of an open $n$-manifold $M$ of nonnegative Ricci curvature with additional stability condition on $\widetilde{M}$, the Riemannian universal cover of $M$. We prove that if any tangent cone of $\widetilde{M}$ at…

Assume that $K$ is an algebraically closed field, $R$ a locally bounded $K$-category, $G$ an admissible group of $K$-linear automorphisms of $R$ and $F:R\rightarrow A$ the Galois $G$-covering functor. In the first part of the paper we show…

For a $k$-vertex graph $F$ and an $n$-vertex graph $G$, an $F$-tiling in $G$ is a collection of vertex-disjoint copies of $F$ in $G$. For $r\in \mathbb{N}$, the $r$-independence number of $G$, denoted $\alpha_r(G)$ is the largest size of a…

Let F be a non-archimedean local field of characteristic zero. In this paper we construct examples of supercuspidal representations showing that the bound $[N/2]$ for the local converse theorem of $GL_N(F)$ is sharp, N general, when the…

We study the Fourier characterisation of strictly positive definite functions on compact abelian groups. Our main result settles the case $G = F \times \mathbb{T}^r$, with $r \in \mathbb{N}$ and $F$ finite. The characterisation obtained for…