The size function for quadratic extensions of complex quadratic fields
Ha Thanh Nguyen Tran1
1 Department of Mathematics and Systems Analysis, Aalto University School of Science, Otakaari 1, 02150 Espoo, Finland
Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 1, pp. 243-259.

The function h0 for a number field is an analogue of the dimension of the Riemann–Roch spaces of divisors on an algebraic curve. In this paper, we prove the conjecture of van der Geer and Schoof about the maximality of h0 at the trivial Arakelov divisor for quadratic extensions of complex quadratic fields.

La fonction h0 pour un corps de nombre est un analogue de la dimension des espaces vectoriels de Riemann–Roch des diviseurs sur une courbe algébrique. Dans cet article, nous montrons une conjecture de van der Geer et Schoof sur la maximalité de h0 au diviseur d’Arakelov trivial pour les extensions quadratiques de corps quadratiques imaginaires.

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DOI : 10.5802/jtnb.978
Classification : 11R16, 11R11, 11R55, 11R40
Mots-clés : Arakelov divisor, effectivity divisor, size function, h0, line bundle

Ha Thanh Nguyen Tran 1

1 Department of Mathematics and Systems Analysis, Aalto University School of Science, Otakaari 1, 02150 Espoo, Finland
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Ha Thanh Nguyen Tran. The size function for quadratic extensions of complex quadratic fields. Journal de théorie des nombres de Bordeaux, Tome 29 (2017) no. 1, pp. 243-259. doi : 10.5802/jtnb.978. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.978/

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