Retract Rationality and Algebraic Tori

Scavia, Federico

Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 173-186

Résumé

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 $p\notin S$.

Détail

DOI : 10.4153/S0008439519000079

Mots-clés : algebraic tori, retract rationality, Noether problem, invertible lattice

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