Vol. 15, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
$p$-adic estimates of exponential sums on curves

Joe Kramer-Miller

Vol. 15 (2021), No. 1, 141–171
Abstract

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 𝔽q of characteristic p 3 and let V X be an affine curve. For a regular function f̄ on V , we may form the L-function L(f̄,V,s) associated to the exponential sums of f̄. In this article, we prove a lower estimate on the Newton polygon of L(f̄,V,s). The estimate depends on the local monodromy of f around each point x X V . This confirms a hope of Deligne that the irregular Hodge filtration forces bounds on p-adic valuations of Frobenius eigenvalues. As a corollary, we obtain a lower estimate on the Newton polygon of a curve with an action of p in terms of local monodromy invariants.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 3.236.212.116 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
$p$-adic cohomology, Artin–Schreier covers, wild ramification, zeta function, Newton polygon, exponential sums
Mathematical Subject Classification 2010
Primary: 14F30
Secondary: 11G20, 11T23
Milestones
Received: 10 October 2019
Revised: 26 May 2020
Accepted: 24 June 2020
Published: 1 March 2021
Authors
Joe Kramer-Miller
Mathematics
University of California Irvine
510V Rowland Hall
Ring Road
Irvine, CA 92612
United States