An arithmetic analogue of Clifford's theorem

@article{Groenewegen2001,
abstract = {Number fields can be viewed as analogues of curves over fields. Here we use metrized line bundles as analogues of divisors on curves. Van der Geer and Schoof gave a definition of a function $h^0$ on metrized line bundles that resembles properties of the dimension $l(D)$ of $H^0(X, \mathcal \{L\}(D))$, where $D$ is a divisor on a curve $X$. In particular, they get a direct analogue of the Rieman-Roch theorem. For three theorems of curves, notably Clifford’s theorem, we will propose arithmetic analogues.},
author = {Groenewegen, Richard P.},
journal = {Journal de théorie des nombres de Bordeaux},
language = {eng},
number = {1},
pages = {143-156},
publisher = {Université Bordeaux I},
title = {An arithmetic analogue of Clifford's theorem},
url = {http://eudml.org/doc/93793},
volume = {13},
year = {2001},
}

TY - JOUR
AU - Groenewegen, Richard P.
TI - An arithmetic analogue of Clifford's theorem
JO - Journal de théorie des nombres de Bordeaux
PY - 2001
PB - Université Bordeaux I
VL - 13
IS - 1
SP - 143
EP - 156
AB - Number fields can be viewed as analogues of curves over fields. Here we use metrized line bundles as analogues of divisors on curves. Van der Geer and Schoof gave a definition of a function $h^0$ on metrized line bundles that resembles properties of the dimension $l(D)$ of $H^0(X, \mathcal {L}(D))$, where $D$ is a divisor on a curve $X$. In particular, they get a direct analogue of the Rieman-Roch theorem. For three theorems of curves, notably Clifford’s theorem, we will propose arithmetic analogues.
LA - eng
UR - http://eudml.org/doc/93793
ER -