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The stable cohomology of the Satake compactification of $\mathcal{A}_g$

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Jiaming Chen, Eduard Looijenga

Algebraic Geometry · Submitted 23 Aug 2015

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

The authors' main claim We find the latter to be impure.

how it is stated · asserted 1.00 read the record →

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arXiv ID1508.05600 (version 2)
Pith IDN6LYP4B3, Pith's permanent record of this paper and its review
CitationEduard Looijenga, Jiaming Chen. "The stable cohomology of the Satake compactification of $\mathcal{A}_g$." arXiv:1508.05600 (2015). https://pith.science/paper/N6LYP4B3
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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, 2,959 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.33 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.91 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Charney and Lee have shown that the rational cohomology of the Satake-Baily-Borel compactification the moduli space of principally polarized abelian varieties of dimension g stabilizes as g grows and they computed this stable cohomology as a Hopf algebra. We give a relatively simple algebro-geometric proof of their theorem that also takes into account the mixed Hodge structure that is present here. We find the latter to be impure.

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 Charney and Lee have shown that the rational cohomology of the Satake-Baily-Borel compactification the moduli space of principally polarized abelian varieties of dimension g stabilizes as g grows and they computed this stable cohomology as a Hopf algebra. background 1.00 0.03 0.10 asserted 1.00
s1 We give a relatively simple algebro-geometric proof of their theorem that also takes into account the mixed Hodge structure that is present here. contribution 0.97 0.95 0.31 asserted 1.00
s2 We find the latter to be impure. result 0.98 0.94 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v2
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  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

Charney and Lee have shown that the rational cohomology of the Satake-Baily-Borel compactification the moduli space of principally polarized abelian varieties of dimension g stabilizes as g grows and they computed this stable cohomology as a Hopf algebra. We give a relatively simple algebro-geometric proof of their theorem that also takes into account the mixed Hodge structure that is present here. We find the latter to be impure.

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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

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