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Integration in valued fields

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Ehud Hrushovski, David Kazhdan

Algebraic Geometry · Submitted 7 Oct 2005

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

The authors' main claim In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers.

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arXiv IDmath/0510133 (version 3)
Pith IDGRRR3SF7, Pith's permanent record of this paper and its review
CitationDavid Kazhdan, Ehud Hrushovski. "Integration in valued fields." arXiv:math/0510133 (2005). https://pith.science/paper/GRRR3SF7
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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, 4,168 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.86 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. This yields new invariants of all definable bijections, as well as invariants of measure preserving bijections.

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 develop a theory of integration over valued fields of residue characteristic zero. contribution 1.00 0.96 0.25 asserted 1.00
s1 In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. result 0.60 0.94 0.46 asserted 1.00
s2 The method depends on an analysis of definable sets up to definable bijections. method 1.00 0.70 0.05 asserted 1.00
s3 We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. result 0.90 0.94 0.20 asserted 1.00
s4 This yields new invariants of all definable bijections, as well as invariants of measure preserving bijections. result 0.90 0.93 0.22 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.85 · evidence from proof or derivation 1.00.

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  • 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 develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of definable sets up to definable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue field and value group. This yields new invariants of all definable bijections, as well as invariants of measure preserving bijections.

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