Joe Kramer-Miller

activity

20162025

most cited

p

-adic estimates of exponential sums on curves

7 citations · 16 across the 12 of their papers we have counts for

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12 papers · 1 filter

math.NT2025

Ekedahl-Oort types of $Z /2 Z$ -covers in characteristic $2$

Jeremy Booher, Steven R. Groen, Joe Kramer-Miller

In this article we study the Ekedahl-Oort types of $Z /2 Z$ -Galois covers $π : Y \to X$ in characteristic two. When the base curve $X$ is ordinary, we show that the E…

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

Transcendence properties of the Artin-Hasse exponential modulo $p$

Joe Kramer-Miller

Let $E_{p} (x)$ denote the Artin-Hasse exponential and let $E_{p} (x)$ denote its reduction modulo $p$ in $F_{p} [[x]]$ . In this article we study transcendence propertie…

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.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.NT2020

Some unlikely intersections between the Torelli locus and Newton strata in $A_{g}$

Joe Kramer-Miller

Let $p$ be an odd prime. What are the possible Newton polygons for a curve in characteristic $p$ ? Equivalently, which Newton strata intersect the Torelli locus in $A_{g}$ ?…

math.NT2020

$p$ -adic estimates of abelian Artin $L$ -functions on curves

Joe Kramer-Miller

The purpose of this article is to prove a "Newton over Hodge" result for finite characters on curves. Let $X$ be a smooth proper curve over a finite field $F_{q}$ of charact…

math.NT2019★ 7 cited

$p$ -adic estimates of exponential sums on curves

Joe Kramer-Miller

The purpose of this article is to prove a ``Newton over Hodge'' result for exponential sums on curves. Let $X$ be a smooth proper curve over a finite field $F_{q}$ of charac…

math.NT2019★ 2 cited

Log-decay $F$ -isocrystals on higher dimensional varieties

Joe Kramer-Miller

Let $k$ be a perfect field of positive characteristic and let $X$ be a smooth irreducible quasi-compact scheme over $k$ . The Drinfeld-Kedlaya theorem states that for an irreducible…

math.NT2018

The monodromy of unit-root $F$ -isocrystals with geometric origin

Joe Kramer-Miller

Let $C$ be a smooth curve over a finite field in characteristic $p$ and let $M$ be an overconvergent $F$ -isocrystal over $C$ . After replacing $C$ with a dense open subset $M$ obtai…

math.NT2016★ 6 cited

The monodromy of $F$ -isocrystals with log-decay

Joe Kramer-Miller

Let U be a smooth geometrically connected affine curve over $F_{p}$ with compactification X. Following Dwork and Katz, a $p$ -adic representation $ρ$ of $π_{1} (U)$ corresponds…

Ekedahl-Oort types of Z/2Z-covers in characteristic 2

Iwasawa theory of Frobenius-torsion class group schemes

Transcendence properties of the Artin-Hasse exponential modulo p

Zeros of the Goss zeta function

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

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

Some unlikely intersections between the Torelli locus and Newton strata in Ag​

p-adic estimates of abelian Artin L-functions on curves

p-adic estimates of exponential sums on curves

Log-decay F-isocrystals on higher dimensional varieties

The monodromy of unit-root F-isocrystals with geometric origin

The monodromy of F-isocrystals with log-decay

Ekedahl-Oort types of $Z /2 Z$ -covers in characteristic $2$

Transcendence properties of the Artin-Hasse exponential modulo $p$

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

Some unlikely intersections between the Torelli locus and Newton strata in $A_{g}$

$p$ -adic estimates of abelian Artin $L$ -functions on curves

$p$ -adic estimates of exponential sums on curves

Log-decay $F$ -isocrystals on higher dimensional varieties

The monodromy of unit-root $F$ -isocrystals with geometric origin

The monodromy of $F$ -isocrystals with log-decay