Geodesic
Retract Rationality and Algebraic Tori
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 173-186

Voir la notice de l'article provenant de la source Cambridge

DOI

For any prime number $p$ and field $k$, we characterize the $p$-retract rationality of an algebraic $k$-torus in terms of its character lattice. We show that a $k$-torus is retract rational if and only if it is $p$-retract rational for every prime $p$, and that the Noether problem for retract rationality for a group of multiplicative type $G$ has an affirmative answer for $G$ if and only if the Noether problem for $p$-retract rationality for $G$ has a positive answer for all $p$. For every finite set of primes $S$ we give examples of tori that are $p$-retract rational if and only if $p\notin S$.
DOI : 10.4153/S0008439519000079
Mots-clés : algebraic tori, retract rationality, Noether problem, invertible lattice 
Scavia, Federico. Retract Rationality and Algebraic Tori. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 173-186. doi: 10.4153/S0008439519000079
@article{10_4153_S0008439519000079,
     author = {Scavia, Federico},
     title = {Retract {Rationality} and {Algebraic} {Tori}},
     journal = {Canadian mathematical bulletin},
     pages = {173--186},
     year = {2020},
     volume = {63},
     number = {1},
     doi = {10.4153/S0008439519000079},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000079/}
}
TY  - JOUR
AU  - Scavia, Federico
TI  - Retract Rationality and Algebraic Tori
JO  - Canadian mathematical bulletin
PY  - 2020
SP  - 173
EP  - 186
VL  - 63
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000079/
DO  - 10.4153/S0008439519000079
ID  - 10_4153_S0008439519000079
ER  - 
%0 Journal Article
%A Scavia, Federico
%T Retract Rationality and Algebraic Tori
%J Canadian mathematical bulletin
%D 2020
%P 173-186
%V 63
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000079/
%R 10.4153/S0008439519000079
%F 10_4153_S0008439519000079

Cité par Sources :