The function 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 at the trivial Arakelov divisor for quadratic extensions of complex quadratic fields.
La fonction 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 au diviseur d’Arakelov trivial pour les extensions quadratiques de corps quadratiques imaginaires.
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Keywords: Arakelov divisor, effectivity divisor, size function, $h^0$, line bundle
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@article{JTNB_2017__29_1_243_0,
author = {Ha Thanh Nguyen Tran},
title = {The size function for quadratic extensions of complex quadratic fields},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {243--259},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {29},
number = {1},
year = {2017},
doi = {10.5802/jtnb.978},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.978/}
}
TY - JOUR AU - Ha Thanh Nguyen Tran TI - The size function for quadratic extensions of complex quadratic fields JO - Journal de théorie des nombres de Bordeaux PY - 2017 SP - 243 EP - 259 VL - 29 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.978/ UR - https://doi.org/10.5802/jtnb.978 DO - 10.5802/jtnb.978 LA - en ID - JTNB_2017__29_1_243_0 ER -
%0 Journal Article %A Ha Thanh Nguyen Tran %T The size function for quadratic extensions of complex quadratic fields %J Journal de théorie des nombres de Bordeaux %D 2017 %P 243-259 %V 29 %N 1 %I Société Arithmétique de Bordeaux %U https://doi.org/10.5802/jtnb.978 %R 10.5802/jtnb.978 %G en %F JTNB_2017__29_1_243_0
Ha Thanh Nguyen Tran. The size function for quadratic extensions of complex quadratic fields. Journal de théorie des nombres de Bordeaux, Volume 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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