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On even $K$-groups over $p$-adic Lie extensions of global function fields

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Meng Fai Lim

Number Theory · Submitted 22 Jul 2024

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

The authors' main claim We also establish a duality between the direct limit and inverse limit of the even $K$-groups.

how it is stated · asserted 1.00 read the record →

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arXiv ID2407.15667 (version 2)
Pith IDMXLH47XH, Pith's permanent record of this paper and its review
CitationMeng Fai Lim. "On even $K$-groups over $p$-adic Lie extensions of global function fields." arXiv:2407.15667 (2024). https://pith.science/paper/MXLH47XH
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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, 3,025 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.50 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Let $p$ be a fixed prime number, and $F$ a global function field of characteristic not equal to $p$. In this paper, we shall study the growth of the Sylow $p$-subgroups of the even $K$-groups in a $p$-adic Lie extension of $F$, where the $p$-adic Lie extension is assumed to contain the cyclotomic $\mathbb{Z}_p$-extension of $F$. We also establish a duality between the direct limit and inverse limit of the even $K$-groups.

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 Let $p$ be a fixed prime number, and $F$ a global function field of characteristic not equal to $p$. background 1.00 0.06 0.02 asserted 0.79
s1 In this paper, we shall study the growth of the Sylow $p$-subgroups of the even $K$-groups in a $p$-adic Lie extension of $F$, where the $p$-adic Lie extension is assumed to contain the cyclotomic $\mathbb{Z}_p$-extension of $F$. contribution 0.99 0.74 0.13 asserted 0.87
s2 We also establish a duality between the direct limit and inverse limit of the even $K$-groups. result 0.82 0.94 0.25 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

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

Let $p$ be a fixed prime number, and $F$ a global function field of characteristic not equal to $p$. In this paper, we shall study the growth of the Sylow $p$-subgroups of the even $K$-groups in a $p$-adic Lie extension of $F$, where the $p$-adic Lie extension is assumed to contain the cyclotomic $\mathbb{Z}_p$-extension of $F$. We also establish a duality between the direct limit and inverse limit of the even $K$-groups.

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What this paper does with the arXiv papers it cites

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 · 3 sentences without a confident label

Compares with 1 paper
  • In [ref] , an analogous result for the Iwasawa cohomology of the Tate module of an abelian variety is proven by the author and his collaborators.

    2405.20963 · Introduction · 0.90

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