69 citations · 200 across the 15 of their papers we have counts for
21 papers
Classically psh and pluriharmonic functions on Berkovich spaces
Walter Gubler, Joseph Rabinoff
First we extend the theory of subharmonic functions on smooth strictly -analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archi…
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.…
Dolbeault Cohomology of Graphs and Berkovich Curves
Walter Gubler, Philipp Jell, Joseph Rabinoff
We introduce real-valued -forms on weighted metric graphs with boundary similar to Lagerberg forms on polyhedral spaces. We compute the Dolbeault cohomology and prove Poinca…
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…
Total -differentials on schemes over
Taylor Dupuy, Eric Katz, Joseph Rabinoff +1
For a scheme defined over the length -typical Witt vectors of a characteristic field, we introduce total -differentials which interpolate between Frobeni…
A rigid analytic proof that the Abel-Jacobi map extends to compact-type models
Taylor Dupuy, Joseph Rabinoff
Let be a non-Archimedean valued field with valuation ring . Let be a -curve with compact type reduction, so its Jacobian extends to an abelian -scheme .…
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…
Diophantine and tropical geometry, and uniformity of rational points on curves
Eric Katz, Joseph Rabinoff, David Zureick-Brown
We describe recent work connecting combinatorics and tropical/non-Archimedean geometry to Diophantine geometry, particularly the uniformity conjectures for rational points on curve…
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 be a complete non-Archimedean field, and let be a…
Uniform bounds for the number of rational points on curves of small Mordell--Weil rank
Eric Katz, Joseph Rabinoff, David Zureick-Brown
Let be a curve of genus over a number field of degree . The conjectural existence of a uniform bound on the number of -rational po…
The Theory of Witt Vectors
Joseph Rabinoff
This is an introduction to the theory of Witt vectors. It includes a construction of the Witt rings, the Frobenius and Verschiebung endomorphisms, the canonical map from W to W^2 (…
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…
Skeletons and tropicalizations
Walter Gubler, Joseph Rabinoff, Annette Werner
Let be a complete, algebraically closed non-archimedean field with ring of integers and let be a -variety. We associate to the data of a strictly semistable $K…
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…
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…
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…
Optimal quotients of Jacobians with toric reduction and component groups
Mihran Papikian, Joseph Rabinoff
Let J be a Jacobian variety with toric reduction over a local field K. Let J -> E be an optimal quotient defined over K, where E is an elliptic curve. We give examples in which the…
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…
Nonarchimedean geometry, tropicalization, and metrics on curves
Matthew Baker, Sam Payne, Joseph Rabinoff
We develop a number of general techniques for comparing analytifications and tropicalizations of algebraic varieties. Our basic results include a projection formula for tropical mu…
Tropical analytic geometry, Newton polygons, and tropical intersections
Joseph Rabinoff
In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem…
Higher-level canonical subgroups for p-divisible groups
Joseph Rabinoff
Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is s…