Representation fields for commutative orders
- [1] Universidad de Chile Departamento de matematicas Facultad de ciencia Casilla 653 Santiago (Chile)
Annales de l’institut Fourier (2012)
- Volume: 62, Issue: 2, page 807-819
- ISSN: 0373-0956
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Abstract
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topArenas-Carmona, Luis. "Representation fields for commutative orders." Annales de l’institut Fourier 62.2 (2012): 807-819. <http://eudml.org/doc/251030>.
@article{Arenas2012,
abstract = {A representation field for a non-maximal order $\mathfrak\{H\}$ in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of $\mathfrak\{H\}$. Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.},
affiliation = {Universidad de Chile Departamento de matematicas Facultad de ciencia Casilla 653 Santiago (Chile)},
author = {Arenas-Carmona, Luis},
journal = {Annales de l’institut Fourier},
keywords = {maximal orders; central simple algebras; spinor genera; spinor class fields},
language = {eng},
number = {2},
pages = {807-819},
publisher = {Association des Annales de l’institut Fourier},
title = {Representation fields for commutative orders},
url = {http://eudml.org/doc/251030},
volume = {62},
year = {2012},
}
TY - JOUR
AU - Arenas-Carmona, Luis
TI - Representation fields for commutative orders
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 2
SP - 807
EP - 819
AB - A representation field for a non-maximal order $\mathfrak{H}$ in a central simple algebra is a subfield of the spinor class field of maximal orders which determines the set of spinor genera of maximal orders containing a copy of $\mathfrak{H}$. Not every non-maximal order has a representation field. In this work we prove that every commutative order has a representation field and give a formula for it. The main result is proved for central simple algebras over arbitrary global fields.
LA - eng
KW - maximal orders; central simple algebras; spinor genera; spinor class fields
UR - http://eudml.org/doc/251030
ER -
References
top- Luis Arenas-Carmona, Spinor class fields for sheaves of lattices Zbl1060.11018
- Luis Arenas-Carmona, Applications of spinor class fields: embeddings of orders and quaternionic lattices, Ann. Inst. Fourier (Grenoble) 53 (2003), 2021-2038 Zbl1060.11018MR2044166
- Luis Arenas-Carmona, Relative spinor class fields: a counterexample, Arch. Math. (Basel) 91 (2008), 486-491 Zbl1158.11048MR2465867
- C. Chevalley, L’arithmétique sur les algèbres de matrices, (1936), Herman, Paris Zbl0014.29006
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- B. Linowitz, T. R. Shemanske, Embedding orders into central simple algebras Zbl1272.11126
- O. T. O’Meara, Introduction to quadratic forms, (1963), Academic press, New York Zbl0107.03301MR152507
- I. Reiner, Maximal orders, (1975), Academic press, London Zbl0305.16001MR1972204
- T. R. Shemanske, Split orders and convex polytopes in buildings, J. Number Theory 130 (2010), 101-115 Zbl1267.11116MR2569844
- A. Weil, Basic Number Theory, (1973), Springer Verlag, Berlin Zbl0267.12001
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