On the relative motive of a commutative group scheme

Annette Huber; Giuseppe Ancona; Simon Pepin Lehalleur

RECORD

On the relative motive of a commutative group scheme

Giuseppe Ancona, Annette Huber, Simon Pepin Lehalleur

Algebraic Geometry · Submitted 11 Sep 2014

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

The authors' main claim We prove a canonical Kuenneth decomposition of the relative motive with rational coefficients of a smooth commutative group scheme over a noetherian finite dimensional base.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,288 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.32 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We prove a canonical Kuenneth decomposition of the relative motive with rational coefficients of a smooth commutative group scheme over a noetherian finite dimensional base. This paper is a follow-up of "On the motive of a commutative algebraic group" arXiv:1312.4171

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We prove a canonical Kuenneth decomposition of the relative motive with rational coefficients of a smooth commutative group scheme over a noetherian finite dimensional base.	result 0.79	0.96	0.95	asserted 1.00
s1	This paper is a follow-up of "On the motive of a commutative algebraic group" arXiv:1312.4171	background 1.00	0.14	0.02	asserted 0.97

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

What was examined, and what was not

sources read

arXiv listing abstract v2

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 prove a canonical Kuenneth decomposition of the relative motive with rational coefficients of a smooth commutative group scheme over a noetherian finite dimensional base. This paper is a follow-up of "On the motive of a commutative algebraic group" arXiv:1312.4171

Human review

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

How the literature uses it

2 arXiv papers cite this in 29 sentences

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

Papers citing it · 19 sentences without a confident label

Uses its method or tool 1 paper

What is more, and highly important for applications, we can construct a class in motivic cohomology for our polylogarithm building on the techniques and results developed in [ref] and [ref] .

Polylogarithm for families of commutative group schemes · Introduction · 0.82

Cites it as support 2 papers

The motivic case is established in [ref] (it follows directly from the description of $M_1(G)$ as the motive induced by $G_$).

Polylogarithm for families of commutative group schemes · Second proof · 0.98
The motive $Σ^∞A_$ is a direct factor of the homological motive of $A$ by Theorem [ref] , so it is geometrically smooth.

Triangulated categories of relative 1-motives · Motives of Deligne $1$-motives · 0.96

Cites it as background 2 papers

In this section, we introduce the relevant definitions and reformulate results from [ref] and [ref] in this language.

Triangulated categories of relative 1-motives · Motives of commutative group schemes · 0.92
This is the same notation as in [ref] , our main reference in the sequel.

Polylogarithm for families of commutative group schemes · Motivic setting · 0.92

What it cites · 17 sentences without a confident label

Uses the method or tool of 1 paper

For this paper, we use indifferently the projective model structures (adapted from presheaves to sheaves) of [ref] or the descent model structures of [ref] .

Triangulated categories of mixed motives · Generalities on relative motives · 0.98

Cites as support 1 paper

Assertion ([ref]) is contained in [ref] and [ref] .

Triangulated categories of mixed motives · Triangulated categories with and without transfers · 0.99

Cites as background 1 paper

There is a sequence of functors (see [ref] for more details on the last one, the infinite $T$-suspension functor) [equation]

Triangulated categories of mixed motives · Generalities on relative motives · 0.81

Discussion

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