Annales de l’institut Fourier (AIF)

Charalambous, Hara

Karagiannis, Kostas

Kontogeorgis, Aristides

Université Grenoble Alpes
ANNALES DE
L’INSTITUT FOURIER
Hara Charalambous,
Kostas Karagiannis & Aristides Kontogeorgis
Corrigendum to “The Relative Canonical Ideal of the
Kummer-Artin Schreier-Witt family of curves”
Tome 75, n
o
5 (2025), p. 1899-1900.
https://doi.org/10.5802/aif.3723
Article mis à disposition par ses auteurs selon les termes de la licence
Creative Commons attribution – pas de modification 3.0 France
http://creativecommons.org/licenses/by-nd/3.0/fr/
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MER S ENN E
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Centre Mersenne pour l’édition scientifique ouverte
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Ann. Inst. Fourier, Grenoble
75, 5 (2025) 1899-1900
CORRIGENDUM TO “THE RELATIVE CANONICAL
IDEAL OF THE KUMMER-ARTIN SCHREIER-WITT
FAMILY OF CURVES”
Annales de l’Institut Fourier, vol. 73 (2023), no 3, 1085-1113
by Hara CHARALAMBOUS,
Kostas KARAGIANNIS & Aristides KONTOGEORGIS
Abstract. — We correct a few typographical erros and ambiguities in the above
mentioned published paper.
Résumé. — Nous corrigeons quelques erreurs typographiques et ambiguïtés dans
l’article publié mentionné ci-dessus.
Dr. Bernhard Köck, who we wish to thank, kindly pointed to us a few
typographical errors and ambiguities, which we address below.
• Page 1088, diagram: the labels of all vertical downwards pointing
arrows should be ⊗RR/mR instead of ⊗RR/m.
• Page 1092, line before eq. (3.1): X0 should be replaced by X0/K.
• Page 1092, line after eq. (3.1): add the sentence “while we let X0/k
be the curve corresponding to the extension of the rational function
field k(x) given by Xp − X = xℓ−pq.”
• Page 1092, next sentence beginning with “Bertin-Mézard”: replace
“curve above” by “curve X0/K”.
• Page 1093, diagram (3.3): the labels of all vertical downwards point-
ing arrows should be ⊗RR/mR instead of ⊗RR/m. Moreover IX0
should be IX0/k both in diagram (3.3) and in the line right below.
• Pages 1093-1094, Theorem 3.2: Replace IX0 by IX0/k once in the
statement and four times in the proof of Theorem 3.2.
• Page 1095, line after eq. (4.1): replace “on the special fiber” by on
“X0/K”. Next line replace ΩX0/k by ΩX0/K .
Keywords: Relative curves, Canonical ideal, Reduction and Lifting.
2020 Mathematics Subject Classification: 14H10, 14F10.
1900 H. Charalambous, K. Karagiannis & A. Kontogeorgis
• Page 1095, last paragraph: replace k by K in three instances (first,
fourth and last line of paragraph).
• Page 1104, line after eq. (5.1): add “X0/k (given by Xp−X = xℓ−pq)
and” after “special fiber”.
• Page 1104, eq. (5.1): change X0 to X0/K.
• Page 1107, line after diagram 5.1: add “⊂ R[{WN,µ}]” after “Gc2”.
• Page 1107, last line: change IX0 to IX0/k.
• Pages 1108 to 1110: throughout Section 5.1 replace k by K and IX0
by IX0/K .
• Page 1109, Remark 5.7: change to “. . . follows by verifying directly
that ϕ0,c(Gc2) = 0”.
• Page 1109, line after Remark 5.7: add “considered over K” after
“Definition 4.3”.
• Page 1111: start the proof with the sentence “The arguments used
in the proofs of Proposition 5.6 and Theorem 5.10, when xi = 0 for
1 ⩽ i ⩽ q − 1 (and i = q if applicable) imply that ⟨(Gc1 ⊗R k) ∪
(Gc2 ⊗R k)⟩ = IX0/k.”
BIBLIOGRAPHY
[1] H. Charalambous, K. Karagiannis & A. Kontogeorgis, “The relative canonical
ideal of the Kummer–Artin Schreier–Witt family of curves”, Ann. Inst. Fourier 73
(2023), no. 3, p. 1085-1113.
Manuscrit reçu le 30 mai 2024,
révisé le 5 septembre 2024,
accepté le 7 octobre 2024.
Hara CHARALAMBOUS
Department of Mathematics, Aristotle University of
Thessaloniki School of Sciences, 54124,
Thessaloniki, Greece
hara@math.auth.gr
Kostas KARAGIANNIS
Department of Mathematics, Aristotle University of
Thessaloniki School of Sciences, 54124,
Thessaloniki, Greece
kkaragia@math.auth.gr
Aristides KONTOGEORGIS
Department of Mathematics, National and
Kapodistrian University of Athens
Panepistimioupolis, 15784 Athens, Greece
kontogar@math.uoa.gr
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