Multiplicative Invariant Fields of Dimension ≤6

The finite subgroups of

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Hlavní autoři: Hoshi, Akinari, Kang, Ming-chang, Yamasaki, Aiichi
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2023
Edice:Memoirs of the American Mathematical Society
Témata:
unramified Brauer groups
crystallographic groups
integral representations
Rationality problems
algebraic tori
Noether’s problem
ISBN:9781470460228, 147046022X
ISSN:0065-9266, 1947-6221
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Abstract The finite subgroups of
AbstractList The finite subgroups of
Author Hoshi, Akinari
Yamasaki, Aiichi
Kang, Ming-chang
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  givenname: Aiichi
  surname: Yamasaki
  fullname: Yamasaki, Aiichi
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Keywords unramified Brauer groups
crystallographic groups
integral representations
Rationality problems
algebraic tori
Noether’s problem
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Language English
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Notes Includes bibliographical references (p. 135-137)
Other authors: Ming-chang Kang, Aiichi Yamasaki
March 2023, volume 283, number 1403 (sixth of 7 numbers)
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TableOfContents Introduction -- Preliminaries and the unramified Brauer groups -- CARAT ID of the <inline-formula content-type="math/mathml"> Z \mathbb {Z} </inline-formula>-classes in dimensions <inline-formula content-type="math/mathml"> 5 5 </inline-formula> and <inline-formula content-type="math/mathml"> 6 6 </inline-formula> -- Proof of Theorem -- Classification of elementary abelian groups <inline-formula content-type="math/mathml"> ( C 2 ) k (C_2)^k </inline-formula> in <inline-formula content-type="math/mathml"> G L n ( Z ) GL_n(\mathbb {Z}) </inline-formula> with <inline-formula content-type="math/mathml"> n ≤ 7 n\leq 7 </inline-formula> -- The case <inline-formula content-type="math/mathml"> G = ( C 2 ) 3 G=(C_2)^3 </inline-formula> with <inline-formula content-type="math/mathml"> H u 2 ( G , M ) ≠ 0 H_u^2(G,M)\neq 0 </inline-formula> -- The case <inline-formula content-type="math/mathml"> G = A 6 G=A_6 </inline-formula> with <inline-formula content-type="math/mathml"> H u 2 ( G , M ) ≠ 0 H_u^2(G,M)\neq 0 </inline-formula> and Noether’s problem for <inline-formula content-type="math/mathml"> N ⋊ A 6 N\rtimes A_6 </inline-formula> -- Some lattices of rank <inline-formula content-type="math/mathml"> 2 n + 2 , 4 n 2n+2, 4n </inline-formula>, and <inline-formula content-type="math/mathml"> p ( p − 1 ) p(p-1) </inline-formula> -- GAP computation: an algorithm to compute <inline-formula content-type="math/mathml"> H u 2 ( G , M ) H_u^2(G,M) </inline-formula> -- Tables: multiplicative invariant fields with non-trivial unramified Brauer groups
Title Multiplicative Invariant Fields of Dimension ≤6
URI https://www.ams.org/memo/1403/
https://cir.nii.ac.jp/crid/1130014393804372135
Volume 283
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