Mathematics > Algebraic Geometry
[Submitted on 19 Oct 2018 (v1), last revised 30 Jun 2019 (this version, v2)]
Title:Retract rationality and algebraic tori
View PDFAbstract: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 $G$ have 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 $p\notin S$.
Submission history
From: Federico Scavia [view email][v1] Fri, 19 Oct 2018 20:34:35 UTC (12 KB)
[v2] Sun, 30 Jun 2019 17:58:55 UTC (14 KB)
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