Related papers: A note on fierce ramification
T. Saito established a ramification theory for ring extensions locally of complete intersection. We show that for a Henselian valuation ring $A$ with field of fractions $K$ and for a finite Galois extension $L$ of $K$, the integral closure…
When the Seiberg-Witten curve of a four-dimensional $\mathcal{N}=2$ supersymmetric gauge theory wraps a Riemann surface as a multi-sheeted cover, a topological constraint requires that in general the curve should develop ramification…
We show that an infinite residually finite boundedly generated group has an infinite chain of finite index subgroups with ranks uniformly bounded, and give (sublinear) upper bounds on the ranks of arbitrary finite index subgroups of…
We establish the boundedness character of solutions of a system of rational difference equations with a variable coefficient
In this note we survey recent results on automorphisms of affine algebraic varieties, infinitely transitive group actions and flexibility. We present related constructions and examples, and discuss geometric applications and open problems.
Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift
We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.
We give an explicit upper bound for the number of equivalence classes of binary forms with rational integral coefficients of given degree and given discriminant, and with given splitting field. Further, we give an explicit upper bound for…
We prove that some of the basic differential functions appearing in the (unramified) theory of arithmetic differential equations, especially some of the basic differential modular forms in that theory, arise from a "ramified situation".…
The minimal ramification problem may be considered as a quantitative version of the inverse Galois problem. For a nontrivial finite group $G$, let $m(G)$ be the minimal integer $m$ for which there exists a Galois extension $N/\mathbb{Q}$…
We define the notion of inseparable coverings of schemes and we propose a ramification formalism for them, along the lines of the classical one. Using this formalism we prove a formula analogous to the classical Riemann-Hurwitz formula for…
We prove non-commutative reciprocity laws on an algebraic surface defined over a perfect field. These reciprocity laws claim the splittings of some central extensions of globally constructed groups over some subgroups constructed by points…
As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey…
In this paper we consider wildly ramified power series, \emph{i.e.}, power series defined over a field of positive characteristic, fixing the origin, where it is tangent to the identity. In this setting we introduce a new invariant under…
We provide an extension of the transference results of Beresnevich and Velani connecting homogeneous and inhomogeneous Diophantine approximation on manifolds and provide bounds for inhomogeneous Diophantine exponents of affine subspaces and…
We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is finite, and that this number is uniformly bounded in any finite type family of base varieties. As a…
In this paper a fourth order equation involving critical growth is considered under Navier boundary condition. We give some topological conditions on a given function to ensure the existence of solutions. Our methods involve the study of…
We give an upper-bound for the $X$-rank of points with respect to a non-degenerate irreducible variety $X$ in the case that sub-generic $X$-rank points generate a hypersurface. We give examples where this bound is sharp and it improves the…
We improve the known Hodge type bound for the exotic cohomology of complete intersections. In the revised version, we included a simplification of our original argument due to Pierre Deligne. The note appears in the C. R. de l'Aca. des Sc.…
We characterize vector lattices in which unbounded order convergence is eventually order bounded. Among other things, the characterization provides a solution to \cite[Probl.23]{Az}.