James Upton

activity

20182024

most citedNewton Polygons of Sums on Curves I: Local-to-Global Theorems

1 citations · 1 across the 7 of their papers we have counts for

collaborators

8 papers

math.NT2024

Iwasawa theory of Frobenius-torsion class group schemes

Jeremy Booher, Bryden Cais, Joe Kramer-Miller +1

We establish a new Iwasawa theory for the kernel of Frobenius on Jacobians of curves in geometric $Z_{p}$ -towers over the projective line in characteristic $p$ , thereby prov…

math.NT2024

Higher a-numbers in $Z_{p}$ -towers via Counting Lattice Points

Jeremy Booher, Jack Hsieh, Rakesh Rivera +3

Booher, Cais, Kramer-Miller and Upton study a class of $Z_{p}$ -tower of curves in characteristic $p$ with ramification controlled by an integer $d$ . In the special case that…

math.NT2023

Zeros of the Goss zeta function

Joe Kramer-Miller, James Upton

Let $X$ be a smooth proper curve over a finite field and let $\infty \in X$ be a closed point. Let $A$ be the ring of functions on $X - \infty$ . The Goss zeta function $ζ_{A}$ of $A$ …

math.NT2022

A cut-by-curves criterion for overconvergent of $F$ -isocrystals

Thomas Grubb, Kiran S. Kedlaya, James Upton

Let $X$ be a smooth scheme over a finite field. It is conjectured that a convergent $F$ -isocrystal on $X$ is overconvergent if its restriction to every curve contained in $X$ is ov…

math.NT2021

Newton Polygons of Sums on Curves II: Variation in $p$ -adic Families

Joe Kramer-Miller, James Upton

In this article we study the behavior of Newton polygons along $Z_{p}$ -towers of curves. Fix an ordinary curve $X$ over a finite field $F_{q}$ of characteristic $p$ .…

math.NT2021★ 1 cited

Newton Polygons of Sums on Curves I: Local-to-Global Theorems

Joe Kramer-Miller, James Upton

The purpose of this article is to study Newton polygons of certain abelian $L$ -functions on curves. Let $X$ be a smooth affine curve over a finite field $F_{q}$ and let $ρ:π…

math.NT2019

Weak Analytic Geometry and a Trace Formula for Families of $p$ -adic Representations

James Upton

The eigencurve is a powerful tool introduced by Coleman and Mazur to study $p$ -adic families of overconvergent modular forms. In this article, we introduce an analogous set of tool…

math.NT2018

Discriminant-Stability in $p$ -adic Lie Towers of Number Fields

James Upton

In this paper we consider a tower of number fields $\dots \supseteq K (1) \supseteq K (0) \supseteq K$ arising naturally from a continuous $p$ -adic representation of $\mathrm{Gal}(\…

Iwasawa theory of Frobenius-torsion class group schemes

Higher a-numbers in Zp​-towers via Counting Lattice Points

Zeros of the Goss zeta function

A cut-by-curves criterion for overconvergent of F-isocrystals

Newton Polygons of Sums on Curves II: Variation in p-adic Families

Newton Polygons of Sums on Curves I: Local-to-Global Theorems

Weak Analytic Geometry and a Trace Formula for Families of p-adic Representations

Discriminant-Stability in p-adic Lie Towers of Number Fields

Higher a-numbers in $Z_{p}$ -towers via Counting Lattice Points

A cut-by-curves criterion for overconvergent of $F$ -isocrystals

Newton Polygons of Sums on Curves II: Variation in $p$ -adic Families

Weak Analytic Geometry and a Trace Formula for Families of $p$ -adic Representations

Discriminant-Stability in $p$ -adic Lie Towers of Number Fields