Published paper
Role in dependence graphs
Proof-critical source
Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
This paper is included only for the following marked statement:
- Lemma 3.1 · journal pp. 145–147The simultaneous approximation/transference estimate imported into Waldschmidt's 1999 lemma.
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Audit summary
Not a correctness certificate. These reports do not replace expert scrutiny or formal verification.
Exact reviewed source
Exact paginated Acta Arithmetica scan hosted on the author's institutional page
Michel Waldschmidt. Approximation simultanée par des produits de puissances de nombres algébriques. Acta Arithmetica 79 (1997), no. 2, 137–162.
Open audited source ↗01Statements2 reported findingsNo statement issues found
The selected simultaneous approximation lemma has the precise transference form required by the 1999 abelian-variety argument.
Lemma 3.1No issue found
The two systems of simultaneous inequalities are quantitatively equivalent
journal pp. 145–147 · Lemma 3.1
The lemma passes in both directions between the primal and dual families of linear-form inequalities with the displayed powers and constants. The dimension indices and exponent reversal agree with the Cassels transference theorem used in its proof.
Lemma 3.2No issue found
Cassels' transference theorem is restated with the needed two directions
journal pp. 145–146 · Lemma 3.2
Waldschmidt explicitly identifies this lemma with Theorem XVII of Chapter V in Cassels and separates its parts A and B. Those are exactly the directions subsequently applied in Lemma 3.1.
02Proofs1 reported findingNo proof issues found
The proof of Lemma 3.1 correctly checks the hypotheses of the represented Cassels transference theorem and propagates the constants.
Proof of Lemma 3.1Correct and complete modulo terminal book source
Both transference directions close
journal pp. 146–147
The proof applies the two halves of Lemma 3.2 to the appropriate coefficient systems and then absorbs dimension-dependent factors into the constants. No reversed inequality or missing parameter range was found. Cassels' published book is the graph's disclosed terminal source.
03Novelty0 reported findingsNo novelty concerns found
No non-novelty findings.