The size function for quadratic extensions of complex quadratic fields

Ha Tran Nguyen Thanh

doi:10.5802/jtnb.978

The size function for quadratic extensions of complex quadratic fields

Ha Tran Nguyen Thanh

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	243-259
Number of pages	17
Journal	Journal de théorie des nombres de Bordeaux
Volume	29
Issue number	1
DOIs	https://doi.org/10.5802/jtnb.978
Publication status	Published - 2017
MoE publication type	A1 Journal article-refereed

Keywords

Arakelov divisor
Effectivity divisor
H
Line bundle
Size function

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10.5802/jtnb.978

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title = "The size function for quadratic extensions of complex quadratic fields",

abstract = "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.",

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T1 - The size function for quadratic extensions of complex quadratic fields

AU - Tran Nguyen Thanh, Ha

PY - 2017

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N2 - 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.

AB - 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.

KW - Arakelov divisor

KW - Effectivity divisor

KW - H

KW - Line bundle

KW - Size function

UR - https://www.scopus.com/pages/publications/85011867634

U2 - 10.5802/jtnb.978

DO - 10.5802/jtnb.978

M3 - Article

AN - SCOPUS:85011867634

SN - 1246-7405

VL - 29

SP - 243

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JO - Journal de théorie des nombres de Bordeaux

JF - Journal de théorie des nombres de Bordeaux

IS - 1

ER -

The size function for quadratic extensions of complex quadratic fields

Abstract

Keywords

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