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Arithmetic fake projective spaces and arithmetic fake grassmannians

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Gopal Prasad, Sai-Kee Yeung

Algebraic Geometry · Submitted 7 Feb 2006

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

The authors' main claim We show that if n>5, PU(n-1,1) does not contain a cocompact arithmetic subgroup with the same Euler-Poincare characteristic (in the sense of C.T.C.

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arXiv IDmath/0602144 (version 4)
Pith IDNHXXH4WF, Pith's permanent record of this paper and its review
CitationGopal Prasad, Sai-Kee Yeung. "Arithmetic fake projective spaces and arithmetic fake grassmannians." arXiv:math/0602144 (2006). https://pith.science/paper/NHXXH4WF
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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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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,610 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.09 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.43 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We show that if n>5, PU(n-1,1) does not contain a cocompact arithmetic subgroup with the same Euler-Poincare characteristic (in the sense of C.T.C. Wall) as the complex projective space of dimension n-1, and show that if n=5, there are at least four such subgroups, which are in fact torsion-free. This, in particular, leads to examples of a fake projective space of dimension 4. Analogous results for arithmetic fake grassmannians Gr(m,n) with n>3 odd are also obtained.

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 that if n>5, PU(n-1,1) does not contain a cocompact arithmetic subgroup with the same Euler-Poincare characteristic (in the sense of C.T.C. result 0.99 0.90 0.42 asserted 1.00
s1 Wall) as the complex projective space of dimension n-1, and show that if n=5, there are at least four such subgroups, which are in fact torsion-free. result 0.99 0.94 0.33 asserted 1.00
s2 This, in particular, leads to examples of a fake projective space of dimension 4. interpretation 0.77 0.90 0.22 asserted 0.99
s3 Analogous results for arithmetic fake grassmannians Gr(m,n) with n>3 odd are also obtained. result 0.85 0.91 0.09 asserted 1.00

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

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  • references and citing sentences
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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

We show that if n>5, PU(n-1,1) does not contain a cocompact arithmetic subgroup with the same Euler-Poincare characteristic (in the sense of C.T.C. Wall) as the complex projective space of dimension n-1, and show that if n=5, there are at least four such subgroups, which are in fact torsion-free. This, in particular, leads to examples of a fake projective space of dimension 4. Analogous results for arithmetic fake grassmannians Gr(m,n) with n>3 odd are also obtained.

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