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Cohomological Milnor formula and Saito's conjecture on characteristic classes

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Enlin Yang, Yigeng Zhao

Algebraic Geometry · Submitted 22 Sep 2022

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

The authors' main claim We confirm the quasi-projective case of Saito's conjecture, namely that the cohomological characteristic classes defined by Abbes and Saito can be computed in terms of the characteristic cycles.

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arXiv ID2209.11086 (version 4)
Pith IDBY3NSWGR, Pith's permanent record of this paper and its review
CitationEnlin Yang, Yigeng Zhao. "Cohomological Milnor formula and Saito's conjecture on characteristic classes." arXiv:2209.11086 (2022). https://pith.science/paper/BY3NSWGR
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,021 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.44 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.32 · mentions code or data availability 0.02.

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

We confirm the quasi-projective case of Saito's conjecture, namely that the cohomological characteristic classes defined by Abbes and Saito can be computed in terms of the characteristic cycles. We construct a cohomological characteristic class supported on the non-acyclicity locus of a separated morphism relatively to a constructible sheaf. As applications of the functorial properties of this class, we prove cohomological analogs of the Milnor formula and the conductor formula for constructible sheaves on (not necessarily smooth) varieties.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We confirm the quasi-projective case of Saito's conjecture, namely that the cohomological characteristic classes defined by Abbes and Saito can be computed in terms of the characteristic cycles. result 0.96 0.94 0.84 asserted 1.00
s1 We construct a cohomological characteristic class supported on the non-acyclicity locus of a separated morphism relatively to a constructible sheaf. contribution 0.98 0.96 0.10 asserted 1.00
s2 As applications of the functorial properties of this class, we prove cohomological analogs of the Milnor formula and the conductor formula for constructible sheaves on (not necessarily smooth) varieties. result 0.91 0.95 0.18 asserted 1.00

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

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  • C citations
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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 confirm the quasi-projective case of Saito's conjecture, namely that the cohomological characteristic classes defined by Abbes and Saito can be computed in terms of the characteristic cycles. We construct a cohomological characteristic class supported on the non-acyclicity locus of a separated morphism relatively to a constructible sheaf. As applications of the functorial properties of this class, we prove cohomological analogs of the Milnor formula and the conductor formula for constructible sheaves on (not necessarily smooth) varieties.

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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

What it cites · 4 sentences without a confident label

Cites as background 1 paper
  • Before the proof, let us recall Abe's reformulation of Laumon's results on local Fourier transform (cf. [ref] ).

    2206.02401 · Section · 0.83

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