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Unstable Motivic Homotopy Theory
Algebraic Topology · Submitted 23 Feb 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.
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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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The abstract, sentence by sentence
We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results. | contribution 0.96 | 0.53 | 0.19 | asserted 0.88 |
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The paper
Original abstract
We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.
Human review
How the literature uses it
6 arXiv papers cite this in 6 sentences
Papers citing it
Cites it as background 6 papers
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We do not use its formal definition and refer the interested reader to [ref] for the definition and to [ref] for an introduction to $^1$-homotopy theory.
Computing A1-Euler numbers with Macaulay2 · Definition of the $^1$-Euler number · 0.99
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The $^1$-degree, first defined by Morel [ref] , provides a foundational tool for solving problems in $^1$-enumerative geometry[For the sake of brevity, we neglect to include exposition of the basic notions used in $^1$-enumerative geometry; instead we refer the reader to the expository paper [ref] , as well as the exposition found throughout the following papers: [ref] .], a field which seeks to resolve enumerative questions over arbitrary fields by wielding the machinery of $^1$-homotopy theory [ref] .
The trace of the local $\mathbf{A}^1$-degree · Introduction · 1.00
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For more information about Grothendieck-Witt rings, see [ref] .
On the EKL-Degree of a Weyl Cover · The Grothendieck-Witt Ring · 1.00
What it cites · 19 sentences without a confident label
Uses the method or tool of 1 paper
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Namely, one can again define a local index using the local degree and then use [ref] to define the Euler number, now an element of $(k)$ [ref] .
An Arithmetic Count of the Lines on a Smooth Cubic Surface · Euler class · 0.89
Compares with 1 paper
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Some comparison results are available between these two Euler classes [ref] [ref] .
Aspects of enumerative geometry with quadratic forms · Euler class · 0.89
Cites as background 2 papers
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Further approaches to defining an Euler class using $A^1$-homotopy theory are found in [ref] [ref] .
Fundamental classes in motivic homotopy theory · Euler class · 0.85
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Further approaches to defining an Euler class using $A^1$-homotopy theory are found in [ref] [ref] .
Motivic Gau{\ss}-Bonnet formulas · Euler class · 0.85
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