On Frobenius incidence varieties of linear subspaces over finite fields

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• 作者：Ichiro Shimada ; ^{shimada@math.sci.hiroshima-u.ac.jp}
• 关键词：14M15 ; 14G15 ; 14C25
• 刊名：Finite Fields and Their Applications
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：18
• 期：2
• 页码：337-361
• 全文大小：303 K

文摘

We define Frobenius incidence varieties by means of the incidence relation of Frobenius images of linear subspaces in a fixed vector space over a finite field, and investigate their properties such as supersingularity, Betti numbers and unirationality. These varieties are variants of the Deligne-Lusztig varieties. We then study the lattices associated with algebraic cycles on them. We obtain a positive-definite lattice of rank 84 that yields a dense sphere packing from a 4-dimensional Frobenius incidence variety in characteristic 2.