Related papers: Logarithmic growth filtrations for $(\varphi,\nabl…

Let $A$ be an abelian variety over a discretely valued field. Edixhoven has defined a filtration on the special fiber of the N\'eron model of $A$ that measures the behaviour of the N\'eron model under tame base change. We interpret the…

We describe a 3-step filtration on all logarithmic abelian varieties with constant degeneration. The obstruction to descending this filtration, as a variegated extension, from logarithmic geometry to algebraic geometry is encoded in a…

Let $X$ be an abelian variety over an algebraically closed field $\mathbf{k}$ and $f$ a quasi-unipotent automorphism of $X$. When $\mathbf{k}$ is the field of complex numbers, Lin, Oguiso, and D.-Q. Zhang provide an explicit formula for the…

For certain pseudo-Anosov flows $\phi$ on closed $3$-manifolds, unpublished work of Agol--Gu\'eritaud produces a veering triangulation $\tau$ on the manifold $M$ obtained by deleting $\phi$'s singular orbits. We show that $\tau$ can be…

Based on the logarithmic algebraic geometry and the theory of Deligne systems, we define an abelian category of $\ell$-adic sheaves with weight filtrations on a logarithmic scheme over a finite field, which is similar to the category of…

We establish a comparison result relating non-archimedean cylinder counts and logarithmic cylinder counts in a smooth affine log Calabi-Yau variety. Using the decomposition theorem and the gluing formula from log Gromov-Witten theory, we…

We prove the logarithmic Sarnak conjecture for sequences of subquadratic word growth. In particular, we show that the Liouville function has at least quadratically many sign patterns. We deduce the main theorem from a variant which bounds…

In this paper, we derive a new $p$-Logarithmic Sobolev inequality and optimal continuous and compact embeddings into Orlicz-type spaces of the function space associated with the logarithmic $p$-Laplacian. As an application of these results,…

This paper develops a systematic approach to infinitesimal variations of Hodge structure for singular and equisingular families by means of logarithmic geometry and residue theory. The central idea is that logarithmic vector fields encode…

We prove the stable degeneration conjecture of log Fano fibration germs formulated by Sun-Zhang. Precisely, we introduce the $\mathbf{H}$-invariant for filtrations over a log Fano fibration germ, and show that there exists a unique…

The present note is devoted to an amendment to a recent paper of Ellenberg, Lawrence and Venkatesh. Roughly speaking, the main result here states the subpolynomial growth of the number of integral points with bounded height of a variety…

We prove the local epsilon-isomorphism conjecture of Fukaya and Kato [FK06] for certain crystalline families of G_Qp-representations. This conjecture can be regarded as a local analogue of the Iwasawa main conjecture for families. Our work…

It was recently suggested -- based on general self-consistency arguments as well as results from the bootstrap (arXiv:2005.07708, arXiv:2007.11539, arXiv:2007.04190) -- that the CFT describing the $Q$-state Potts model is logarithmic for…

Let $K$ be a field which is complete for a discrete valuation. We prove a logarithmic version of the N\'eron-Ogg-Shafarevich criterion: if $A$ is an abelian variety over $K$ which is cohomologically tame, then $A$ has good reduction in the…

In this article we study polynomial logarithmic $q$-forms on a projective space and characterize those that define singular foliations of codimension $q$. Our main result is the algebraic proof of their infinitesimal stability when $q=2$…

We introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and the ordinary normal sheaf of the foliation, and measure the…

In [BS07] Breuil and Schneider formulated a conjecture on the equivalence of the existence of invariant norms on certain $p$-adically locally algebraic representations of $GL_n(F)$ and the existence of certain de-Rham representations of…

Since their introduction by Erd\H{o}s in 1950, covering systems (that is, finite collections of arithmetic progressions that cover the integers) have been extensively studied, and numerous questions and conjectures have been posed regarding…

We provide a simple and new induction based treatment of the problem of distinguishing cusp forms from the growth of the Fourier coefficients of modular forms. Our approach gives the best possible ranges of the weights for this problem, and…

We establish (Theorem 3.6) polynomial-growth estimates for the Fourier coefficients of holomorphic logarithmic vector-valued modular forms.