Ramification groups and Artin conductors of radical extensions of ℚ

Filippo Viviani[1]

  • [1] Universita’ degli studi di Roma Tor Vergata Dipartimento dimatematica via della ricerca scientifica 1 00133 Roma, Italy

Journal de Théorie des Nombres de Bordeaux (2004)

  • Volume: 16, Issue: 3, page 779-816
  • ISSN: 1246-7405

Abstract

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We study the ramification properties of the extensions ℚ ( ζ m , a m ) / ℚ under the hypothesis that m is odd and if p ∣ m than either p ∤ v p ( a ) or p v p ( m ) ∣ v p ( a ) ( v p ( a ) and v p ( m ) are the exponents with which p divides a and m ). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we give formulas for the p -adique valuation of the discriminant of the studied global extensions with m = p r .

How to cite

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Viviani, Filippo. "Ramification groups and Artin conductors of radical extensions of $\mathbb{Q}$." Journal de Théorie des Nombres de Bordeaux 16.3 (2004): 779-816. <http://eudml.org/doc/249272>.

@article{Viviani2004,
abstract = {We study the ramification properties of the extensions $\mathbb\{Q\}(\zeta _m,\@root m \of \{a\})/\mathbb\{Q\}$ under the hypothesis that $m$ is odd and if $p\mid m$ than either $p\nmid v_p(a)$ or $p^\{v_p(m)\}\mid v_p(a)$ ($v_p(a)$ and $v_p(m)$ are the exponents with which $p$ divides $a$ and $m$). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we give formulas for the $p$-adique valuation of the discriminant of the studied global extensions with $m=p^r$.},
affiliation = {Universita’ degli studi di Roma Tor Vergata Dipartimento dimatematica via della ricerca scientifica 1 00133 Roma, Italy},
author = {Viviani, Filippo},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {ramification groups; Artin conductors},
language = {eng},
number = {3},
pages = {779-816},
publisher = {Université Bordeaux 1},
title = {Ramification groups and Artin conductors of radical extensions of $\mathbb\{Q\}$},
url = {http://eudml.org/doc/249272},
volume = {16},
year = {2004},
}

TY - JOUR
AU - Viviani, Filippo
TI - Ramification groups and Artin conductors of radical extensions of $\mathbb{Q}$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2004
PB - Université Bordeaux 1
VL - 16
IS - 3
SP - 779
EP - 816
AB - We study the ramification properties of the extensions $\mathbb{Q}(\zeta _m,\@root m \of {a})/\mathbb{Q}$ under the hypothesis that $m$ is odd and if $p\mid m$ than either $p\nmid v_p(a)$ or $p^{v_p(m)}\mid v_p(a)$ ($v_p(a)$ and $v_p(m)$ are the exponents with which $p$ divides $a$ and $m$). In particular we determine the higher ramification groups of the completed extensions and the Artin conductors of the characters of their Galois group. As an application, we give formulas for the $p$-adique valuation of the discriminant of the studied global extensions with $m=p^r$.
LA - eng
KW - ramification groups; Artin conductors
UR - http://eudml.org/doc/249272
ER -

References

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