Indecomposable quadratic lattices over global function fields

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• 作者：Ruiqing Wang ^{rqwang@zzia.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：11E12 ; 11R29
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：160
• 期：Complete
• 页码：516-525
• 全文大小：577 K

文摘

In this paper, we prove that there exists an indecomposable lattice of rank 5 over a Hasse domain of any rational function field in which −1 is not a square, which solves a problem proposed by Gerstein. We also construct three concrete indecomposable lattices of rank 6 and rank 5 over a Hasse domain of the rational function field F₇(x)$F_7(x)$.