Pith. Sign in

RECORD

Generic Extensions and Generic Polynomials for Linear Algebraic Groups

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Eric Y. Chen, J.T. Ferrara, Liam Mazurowski

Number Theory · Submitted 16 Jan 2016

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

The authors' main claim We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1601.04201 (version 1)
Pith ID3JYRLWKH, Pith's permanent record of this paper and its review
CitationEric Y. Chen, J.T. Ferrara, Liam Mazurowski. "Generic Extensions and Generic Polynomials for Linear Algebraic Groups." arXiv:1601.04201 (2016). https://pith.science/paper/3JYRLWKH
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, 4,259 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.65 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.68 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields satisfying certain conditions on cohomology. In particular, we use our techniques to study constructions for unipotent groups, certain algebraic tori, and certain split semisimple groups. An attractive consequence of our work is the construction of generic polynomials in the optimal number of parameters for all cyclic 2-groups over all fields of positive characteristic. This contrasts with a theorem of Lenstra, which states no cyclic 2-group of order $\ge 8$ has a generic polynomial over $\mathbb{Q}$.

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 We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. contribution 0.71 0.96 0.87 asserted 1.00
s1 The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields satisfying certain conditions on cohomology. method 0.41 0.79 0.08 asserted 0.98
s2 In particular, we use our techniques to study constructions for unipotent groups, certain algebraic tori, and certain split semisimple groups. contribution 0.93 0.91 0.07 asserted 0.99
s3 An attractive consequence of our work is the construction of generic polynomials in the optimal number of parameters for all cyclic 2-groups over all fields of positive characteristic. result 0.73 0.95 0.27 asserted 1.00
s4 This contrasts with a theorem of Lenstra, which states no cyclic 2-group of order $\ge 8$ has a generic polynomial over $\mathbb{Q}$. background 0.60 0.03 0.05 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from proof or derivation 1.00.

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

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields satisfying certain conditions on cohomology. In particular, we use our techniques to study constructions for unipotent groups, certain algebraic tori, and certain split semisimple groups. An attractive consequence of our work is the construction of generic polynomials in the optimal number of parameters for all cyclic 2-groups over all fields of positive characteristic. This contrasts with a theorem of Lenstra, which states no cyclic 2-group of order $\ge 8$ has a generic polynomial over $\mathbb{Q}$.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.