Joseph Rabinoff

activity

20092025

most citedOn the structure of nonarchimedean analytic curves

69 citations · 200 across the 15 of their papers we have counts for

collaborators

Showing math.AGShow all

16 papers · 1 filter

math.AG2025

Classically psh and pluriharmonic functions on Berkovich spaces

Walter Gubler, Joseph Rabinoff

First we extend the theory of subharmonic functions on smooth strictly $k$ -analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archi…

math.AG2025

On semipositive piecewise linear functions in non-archimedean analytic geometry

Walter Gubler, Joseph Rabinoff

In this paper, we generalize results on Zhang's semipositive model metrics from the algebraic setting to strictly analytic spaces over a non-trivially valued non-Archimedean field.…

math.AG2021

Dolbeault Cohomology of Graphs and Berkovich Curves

Walter Gubler, Philipp Jell, Joseph Rabinoff

We introduce real-valued $(p, q)$ -forms on weighted metric graphs with boundary similar to Lagerberg forms on polyhedral spaces. We compute the Dolbeault cohomology and prove Poinca…

math.AG2021

Forms on Berkovich spaces based on harmonic tropicalizations

Walter Gubler, Philipp Jell, Joseph Rabinoff

We introduce tropical skeletons for Berkovich spaces based on results of Ducros. Then we study harmonic functions on good strictly analytic spaces over a non-trivially valued non-A…

math.AG2017

Total $p$ -differentials on schemes over $Z / p^{2}$

Taylor Dupuy, Eric Katz, Joseph Rabinoff +1

For a scheme $X$ defined over the length $2$ $p$ -typical Witt vectors $W_{2} (k)$ of a characteristic $p$ field, we introduce total $p$ -differentials which interpolate between Frobeni…

math.AG2017

A rigid analytic proof that the Abel-Jacobi map extends to compact-type models

Taylor Dupuy, Joseph Rabinoff

Let $K$ be a non-Archimedean valued field with valuation ring $R$ . Let $C_{η}$ be a $K$ -curve with compact type reduction, so its Jacobian $J_{η}$ extends to an abelian $R$ -scheme $J$ .…

math.AG2017★ 11 cited

Non-Archimedean and tropical theta functions

Tyler Foster, Joseph Rabinoff, Farbod Shokrieh +1

We define a tropicalization procedure for theta functions on abelian varieties over a non-Archimedean field. We show that the tropicalization of a non-Archimedean theta function is…

math.AG2015

Tropical Skeletons

Walter Gubler, Joseph Rabinoff, Annette Werner

In this paper, we study the interplay between tropical and analytic geometry for closed subschemes of toric varieties. Let $K$ be a complete non-Archimedean field, and let $X$ be a…

math.AG2014★ 42 cited

Lifting harmonic morphisms II: tropical curves and metrized complexes

Omid Amini, Matthew Baker, Erwan Brugallé +1

In this paper we prove several lifting theorems for morphisms of tropical curves. We interpret the obstruction to lifting a finite harmonic morphism of augmented metric graphs to a…

math.AG2014

Skeletons and tropicalizations

Walter Gubler, Joseph Rabinoff, Annette Werner

Let $K$ be a complete, algebraically closed non-archimedean field with ring of integers $K^{\circ}$ and let $X$ be a $K$ -variety. We associate to the data of a strictly semistable $K…

math.AG2014★ 69 cited

On the structure of nonarchimedean analytic curves

Matthew Baker, Sam Payne, Joseph Rabinoff

Let K be an algebraically closed, complete nonarchimedean field and let X be a smooth K-curve. In this paper we elaborate on several aspects of the structure of the Berkovich analy…

math.AG2013★ 3 cited

The skeleton of the Jacobian, the Jacobian of the skeleton, and lifting meromorphic functions from tropical to algebraic curves

Matthew Baker, Joseph Rabinoff

Let K be an algebraically closed field which is complete with respect to a nontrivial, non-Archimedean valuation and let Λbe its value group. Given a smooth, proper, connected K-cu…

math.AG2013★ 19 cited

Lifting harmonic morphisms I: metrized complexes and Berkovich skeleta

Omid Amini, Matthew Baker, Erwan Brugallé +1

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 con…

math.AG2011★ 1 cited

Lifting non-proper tropical intersections

Brian Osserman, Joseph Rabinoff

We prove that if X, X' are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical inters…

math.AG2011

Nonarchimedean geometry, tropicalization, and metrics on curves