James Upton

activity

20182022

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

1 citations · 1 across the 4 of their papers we have counts for

collaborators

5 papers

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}(\…

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

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