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Retract Rationality and Algebraic Tori
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 1 / March 2020
- Published online by Cambridge University Press:
- 18 July 2019, pp. 173-186
- Print publication:
- March 2020
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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 
$p\notin S$.
RAMIFICATION IN KUMMER EXTENSIONS ARISING FROM ALGEBRAIC TORI
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 2 / October 2017
- Published online by Cambridge University Press:
- 17 August 2017, pp. 196-204
- Print publication:
- October 2017
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