Metric uniformization of morphisms of Berkovich curves via p-adic differential equations

Baldassarri, Francesco; Bojković, Velibor

doi:10.1007/s11856-021-2147-8

Cited by 2 publications

(2 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We collect some of the more obvious properties of an n-radial morphism f : D 1 → D 2 . For a more detailed study we refer to [1].…”

Section: Suppose We Are Given An Elementmentioning

confidence: 99%

Canonical factorizations of morphisms of Berkovich curves

Bojković¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

We prove that, for certain extensions of valued fields which admit a sensible theory of ramification groups, there exist canonical towers that correspond to the break-points of their Herbrand function. In particular, each of the intermediate field extensions in the tower has a Herbrand function with only one break-point and there is at most one extension with trivial Herbrand function.We apply the result to the setting of finite morphisms of Berkovich curves where we prove the existence of canonical local and global factorization of such morphisms according to their metric properties.Finally, we use the canonical factorizations to prove harmonicity properties finite morphisms satisfy at each type 2 point: formulas that can be regarded as a refinement of the Riemann-Hurwitz formula for such morphisms.

show abstract

“…We collect some of the more obvious properties of an n-radial morphism f : D 1 → D 2 . For a more detailed study we refer to [1].…”

Section: Suppose We Are Given An Elementmentioning

confidence: 99%

Canonical factorizations of morphisms of Berkovich curves

Bojković¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…to study the ramification properties of certain extensions of valued fields that appear in the context of Berkovich curves as well as in establishing general "laplacian" formula for the multiradius of convergence of differential modules on Berkovich curves. Furthermore, it has been used in [1] to study metric properties and skeleta of finite morphisms of Berkovich analytic curves.…”

Section: Introductionmentioning

confidence: 99%

Optimal bases for direct images of $p$-adic differential modules over discs

Bojković

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Let (k, |•|) be a complete and algebraically closed valued field extension of (Qp, |•|p). Given a finite morphism ϕ : D 1 → D 2 of unit discs over k, a differential module (M, D) on D 1 and a point b ∈ D 2 (k), we construct explicitly an optimal basis of space of horizontal elements for the direct image ϕ * (M, D) at b in terms of the suitable chosen optimal bases of (M, D) at preimages of b by ϕ and ramification properties of the morphism.

show abstract

Metric uniformization of morphisms of Berkovich curves via p-adic differential equations

Cited by 2 publications

References 22 publications

Canonical factorizations of morphisms of Berkovich curves

Canonical factorizations of morphisms of Berkovich curves

Optimal bases for direct images of $p$-adic differential modules over discs

Contact Info

Product

Resources

About