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Lifting laws and arithmetic invariant theory

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Aaron Pollack

Number Theory · Submitted 27 Sep 2016

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

The authors' main claim We prove a handful of these lifting laws, and show how they can be used to help solve certain problems in arithmetic invariant theory.

how it is stated · asserted 1.00 read the record →

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arXiv ID1609.08273 (version 4)
Pith IDYIGOGUJB, Pith's permanent record of this paper and its review
CitationAaron Pollack. "Lifting laws and arithmetic invariant theory." arXiv:1609.08273 (2016). https://pith.science/paper/YIGOGUJB
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,942 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.71 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

In this paper we discuss lifting laws which, roughly, are ways of "lifting" elements of the open orbit of one prehomogeneous vector space to elements of the minimal nonzero orbit of another prehomogeneous vector space. We prove a handful of these lifting laws, and show how they can be used to help solve certain problems in arithmetic invariant theory. Of the results contained in this article are twisted versions of certain parametrization theorems of Bhargava.

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 In this paper we discuss lifting laws which, roughly, are ways of "lifting" elements of the open orbit of one prehomogeneous vector space to elements of the minimal nonzero orbit of another prehomogeneous vector space. background 0.85 0.24 0.07 asserted 0.82
s1 We prove a handful of these lifting laws, and show how they can be used to help solve certain problems in arithmetic invariant theory. contribution 0.90 0.96 0.61 asserted 1.00
s2 Of the results contained in this article are twisted versions of certain parametrization theorems of Bhargava. result 0.47 0.68 0.16 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 1.00.

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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

In this paper we discuss lifting laws which, roughly, are ways of "lifting" elements of the open orbit of one prehomogeneous vector space to elements of the minimal nonzero orbit of another prehomogeneous vector space. We prove a handful of these lifting laws, and show how they can be used to help solve certain problems in arithmetic invariant theory. Of the results contained in this article are twisted versions of certain parametrization theorems of Bhargava.

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