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Current results on Newton polygons of curves

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Rachel Pries

Number Theory · Submitted 12 Jun 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The chapter ends with a new theorem, in which I prove that questions about the geometry of the Newton polygon and Ekedahl-Oort strata can be reduced to the case of $p$-rank $0$.

how it is stated · asserted 1.00 read the record →

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arXiv ID1806.04654 (version 1)
Pith IDNZ37WEED, Pith's permanent record of this paper and its review
CitationRachel Pries. "Current results on Newton polygons of curves." arXiv:1806.04654 (2018). https://pith.science/paper/NZ37WEED
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,354 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.23 · compares with prior results 0.31 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

There are open questions about which Newton polygons and Ekedahl-Oort types occur for Jacobians of smooth curves of genus $g$ in positive characteristic $p$. In this chapter, I survey the current state of knowledge about these questions. I include a new result, joint with Karemaker, which verifies, for each odd prime $p$, that there exist supersingular curves of genus $g$ defined over $\overline{{\mathbb F}}_p$ for infinitely many new values of $g$. I sketch a proof of Faber and Van der Geer's theorem about the geometry of the $p$-rank stratification of the moduli space of curves. The chapter ends with a new theorem, in which I prove that questions about the geometry of the Newton polygon and Ekedahl-Oort strata can be reduced to the case of $p$-rank $0$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 There are open questions about which Newton polygons and Ekedahl-Oort types occur for Jacobians of smooth curves of genus $g$ in positive characteristic $p$. background 0.55 0.04 0.03 asserted 0.99
s1 In this chapter, I survey the current state of knowledge about these questions. contribution 0.68 0.60 0.03 asserted 0.81
s2 I include a new result, joint with Karemaker, which verifies, for each odd prime $p$, that there exist supersingular curves of genus $g$ defined over $\overline{{\mathbb F}}_p$ for infinitely many new values of $g$. result 0.74 0.96 0.14 asserted 1.00
s3 I sketch a proof of Faber and Van der Geer's theorem about the geometry of the $p$-rank stratification of the moduli space of curves. contribution 0.59 0.43 0.04 asserted 0.97
s4 The chapter ends with a new theorem, in which I prove that questions about the geometry of the Newton polygon and Ekedahl-Oort strata can be reduced to the case of $p$-rank $0$. result 0.84 0.95 0.63 asserted 1.00

What kind of paper the classifier reports this is: review 0.73 · evidence from proof or derivation 0.88.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

There are open questions about which Newton polygons and Ekedahl-Oort types occur for Jacobians of smooth curves of genus $g$ in positive characteristic $p$. In this chapter, I survey the current state of knowledge about these questions. I include a new result, joint with Karemaker, which verifies, for each odd prime $p$, that there exist supersingular curves of genus $g$ defined over $\overline{{\mathbb F}}_p$ for infinitely many new values of $g$. I sketch a proof of Faber and Van der Geer's theorem about the geometry of the $p$-rank stratification of the moduli space of curves. The chapter ends with a new theorem, in which I prove that questions about the geometry of the Newton polygon and Ekedahl-Oort strata can be reduced to the case of $p$-rank $0$.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 2 sentences without a confident label

Cites as support 1 paper
Cites as background 1 paper

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