Related papers: Lifting problem for minimally wild covers of Berko…

Given a generically \'etale morphism $f\colon Y\to X$ of quasi-smooth Berkovich curves, we define a different function $\delta_f\colon Y\to[0,1]$ that measures the wildness of the topological ramification locus of $f$. This provides a new…

We consider a finite \'etale morphism $f:Y \to X$ of quasi-smooth Berkovich curves over a complete nonarchimedean non-trivially valued field $k$, assumed algebraically closed and of characteristic 0, and a skeleton…

Let K be an algebraically closed, complete non-Archimedean field. The purpose of this paper is to carefully study the extent to which finite morphisms of algebraic K-curves are controlled by certain combinatorial objects, called skeleta. A…

In non-archimedean setting, we establish a Lehto--Virtanen-type theorem for a morphism from the punctured Berkovich closed unit disk $\overline{\mathsf{D}}\setminus\{0\}$ in the Berkovich affine line to the Berkovich projective line…

In arXiv:1711.10132 a new approximating invariant ${\mathsf{TC}}^{\mathcal{D}}$ for topological complexity was introduced called $\mathcal{D}$-topological complexity. In this paper, we explore more fully the properties of…

The canonical trace and the Wodzicki residue on classical pseudodifferential operators on a closed manifold are characterised by their locality and shown to be preserved under lifting to the universal covering as a result of their local…

Given a quasi-smooth Berkovich curve $X$ admitting a finite triangulation, finitely many disjoint open annuli $A_1,\dots,A_n$ in $X$ that are not precompact, and for each $i=1,\dots, n$, an analytic function $f_i$ (resp. differential form…

We develop a lifting theory for the exponential map of semi-Riemannian manifolds that overcomes the classical obstruction caused by its singularities. We show that every smooth path in the manifold admits, up to a nondecreasing…

We give a global, intrinsic, and co-ordinate-free quantization formalism for Gromov-Witten invariants and their B-model counterparts, which simultaneously generalizes the quantization formalisms described by Witten, Givental, and…

We introduce the notion of interlaced weak ditalgebras and apply reduction procedures to their module categories to prove a tame-wild dichotomy for the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules for an arbitrary finite…

We study the combination of two o-minimal extensions of the theory of real closed fields: one by a T-convex subring and the other by a T-derivation. Let T be a complete, model complete o-minimal extension of RCF. We show that the combined…

Let $f(x)$, $x\in\mathbb R^2$, be a piecewise smooth function with a jump discontinuity across a smooth surface $\mathcal S$. Let $f_{\Lambda\epsilon}$ denote the Lambda tomography (LT) reconstruction of $f$ from its discrete Radon data…

In this paper, we explore the connections between the Minimal Model Program and the theory of Berkovich spaces. Let $k$ be a field of characteristic zero and let $X$ be a smooth and proper $k((t))$-variety with semi-ample canonical divisor.…

Let $k$ be a non-archimedean complete field. We prove a substitute for the reduced fiber theorem (of Bosch, L\"utkebohmert and Raynaud) that holds for every morphism $Y\to X$ flat and with geometrically reduced fibers between $k$-affinoid…

The Kawazumi-Zhang invariant $\varphi$ for compact genus-two Riemann surfaces was recently shown to be a eigenmode of the Laplacian on the Siegel upper half-plane, away from the separating degeneration divisor. Using this fact and the known…

We generalise Hinich's Theorem of descent of Deligne groupoids to the case where the dgLas involved have no negative cohomology. We apply this result to study the infinitesimal deformations of a morphism $\alpha: {\mathcal F} \to {\mathcal…

This article studies descent theory in the setting of Berkovich spaces. We give sufficient conditions for a given fibered category over the category of k-affinoid algebras to be a stack for the Berkovich analogue of the faithfully-flat…

We show that if a differential equations $\mathscr{F}$ over a quasi-smooth Berkovich curve $X$ has a certain compatibility condition with respect to an automorphism $\sigma$ of $X$, and if the automorphism is sufficiently close to the…

We construct a canonical stabilizer reduction $\widetilde{X}$ for any derived $1$-algebraic stack $X$ over $\mathbb{C}$ as a sequence of derived Kirwan blow-ups, under mild natural conditions that include the existence of a good moduli…

Given a hypersurface defined by $f$ in a smooth complex algebraic variety $X$, and a point $P$ on this hypersurface, we consider the invariant $\beta_P(f)$ given by the log canonical threshold at $P$ of ${\mathfrak m}_P\cdot J_f$, where…