Related papers: Differential modules on p-adic polyannuli

Using a local construction from a previous paper, we exhibit a numerical invariant, the differential Swan conductor, for an isocrystal on a variety over a perfect field of positive characteristic overconvergent along a boundary divisor;…

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local…

We study differential $p$-forms on non-smooth and possibly fractal metric measure spaces, endowed with a local Dirichlet form. Using this local Dirichlet form, we prove a result on the localization of antisymmetric functions of $p+1$…

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

We study the Picard groups of moduli spaces in positive characteristics and we give a "$p$-adic" proof that the Picard group of moduli of vector bundles of fixed determinant is isomorphic to the group of integers. Along the way we prove…

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono. As our goal is just to illustrate how…

Differentials on Riemann surfaces correspond to translation surfaces with conical singularities, and affine transformations acting on them preserve the orders of these singularities. This viewpoint allows the moduli spaces of differentials…

We describe the moduli spaces of morphisms between polarized complex abelian varieties. The discrete invariants, derived from a Poincare' decomposition of morphisms, are the types of polarizations and of lattice homomorphisms occurring in…

We analyze the moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP^1 sigma model in 1+2 dimensions. After carefully reviewing the commutative results of Ward and Ruback, the noncommutative K"ahler…

This paper works out the structure of singular points of p-adic differential equations (i.e. differential modules over the ring of functions analytic in some annulus with external radius 1). Surprisingly results look like in the formal case…

We complete our proof that given an overconvergent F-isocrystal on a variety over a field of positive characteristic, one can pull back along a suitable generically finite cover to obtain an isocrystal which extends, with logarithmic…

We study moduli of holomorphic vector bundles on non-compact varieties. We discuss filtrability and algebraicity of bundles and calculate dimensions of local moduli. As particularly interesting examples, we describe numerical invariants of…

The goal of this paper is to study certain p-adic differential operators on automorphic forms on U(n,n). These operators are a generalization to the higher-dimensional, vector-valued situation of the p-adic differential operators…

In this paper, we study the moduli spaces of parabolic connections with a quadratic differential. We endow these moduli spaces with symplectic structures by using the fundamental 2-forms on the moduli spaces of parabolic connections (which…

We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not…

Let $X$ be a smooth polarized algebraic surface over the compex number field. We discuss the invariants obtained from the moduli stacks of semistable sheaves of arbitrary ranks on $X$. For that purpose, we construct the virtual fundamental…

We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…

We introduce differential characters of Drinfeld modules. These are function-field analogues of Buium's p-adic differential characters of elliptic curves and of Manin's differential characters of elliptic curves in differential algebra,…

We study framed translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces, for which a horizontal separatrix is marked for each pole or zero. Such geometric structures naturally appear when studying flat…

We study the $p$-rank stratification of the moduli space $\mathcal{ASW}_{(d_1,d_2,\ldots,d_n)}$, which represents $\mathbb{Z}/p^n$-covers in characteristic $p>0$ whose $\mathbb{Z}/p^i$-subcovers have conductor $d_i$. In particular, we…