@article{Illengo2008,
abstract = {Let $\{p\ne 2\}$ be a prime and let $G$ be a $p$-group of matrices in $\{\{\{\mathrm\{SL\}\}\}_n(\mathbb\{Z\})\}$, for some integer $n$. In this paper we show that, when $\{n<3(p-1)\}$, a certain subgroup of the cohomology group $\{H^1(G,\{\{\mathbb\{F\}\}\}_p^n)\}$ is trivial. We also show that this statement can be false when $\{n\ge 3(p-1)\}$. Together with a result of Dvornicich and Zannier (see [2]), we obtain that any algebraic torus of dimension $\{n<3(p-1)\}$ enjoys a local-global principle on divisibility by $p$.},
affiliation = {Scuola Normale Superiore Piazza dei Cavalieri 7 56126 Pisa, Italia},
author = {Illengo, Marco},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {cohomology of groups; algebraic tori; local-global divisibility},
language = {eng},
number = {2},
pages = {327-334},
publisher = {Université Bordeaux 1},
title = {Cohomology of integer matrices and local-global divisibility on the torus},
url = {http://eudml.org/doc/10838},
volume = {20},
year = {2008},
}
TY - JOUR
AU - Illengo, Marco
TI - Cohomology of integer matrices and local-global divisibility on the torus
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2008
PB - Université Bordeaux 1
VL - 20
IS - 2
SP - 327
EP - 334
AB - Let ${p\ne 2}$ be a prime and let $G$ be a $p$-group of matrices in ${{{\mathrm{SL}}}_n(\mathbb{Z})}$, for some integer $n$. In this paper we show that, when ${n<3(p-1)}$, a certain subgroup of the cohomology group ${H^1(G,{{\mathbb{F}}}_p^n)}$ is trivial. We also show that this statement can be false when ${n\ge 3(p-1)}$. Together with a result of Dvornicich and Zannier (see [2]), we obtain that any algebraic torus of dimension ${n<3(p-1)}$ enjoys a local-global principle on divisibility by $p$.
LA - eng
KW - cohomology of groups; algebraic tori; local-global divisibility
UR - http://eudml.org/doc/10838
ER -
