Lattices in finite fields

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• 作者：Yoshinori Hamahata (1)
  
  1. Institute for Teaching and Learning ; Ritsumeikan University ; 1-1-1 Noji-higashi ; Kusatsu ; Shiga聽 ; 525-8577 ; Japan
  
• 关键词：Lattices ; $$j$$ j ; Invariants ; Finite fields ; 12E20 ; 12E10 ; 06B25
• 刊名：Beitr?ge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：56
• 期：1
• 页码：313-324
• 全文大小：185 KB
• 参考文献：1. Deligne, P., Husem枚ller, D.: Survey of Drinfeld modules. Contemp. Math. 67, 25鈥?1 (1987) CrossRef
  2. Gekeler, E.-U.: Zur Arithmetik von Drinfeld-Moduln. Math. Ann. 262, 167鈥?82 (1983) CrossRef
  3. Gekeler, E.-U.: Finite modular forms. Finite Fields Appl. 7, 553鈥?72 (2001) CrossRef
  4. Goss, D.: \(\pi \) -adic Eisenstein series for function fields. Compositio Math. 41, 3鈥?8 (1980)
  5. Goss, D.: Basic Structures of Function Field Arithmetic. Springer, Berlin (1998)
  6. Hamahata, Y.: The values of \(J\) -invariants for Drinfeld modules. Manuscripta Math. 112, 93鈥?08 (2003) CrossRef
  7. Potemine, I.Y.: Minimal terminal \(\mathbb{Q}\) -factorial models of Drinfeld coarse moduli schemes. Math. Phys. Anal. Geom. 1, 171鈥?91 (1998) CrossRef
  8. Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Princeton University Press, Princeton
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra
  Convex and Discrete Geometry
  Geometry
  Algebraic Geometry
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2191-0383

文摘

In this paper, we consider lattices in \(\overline{\mathbb{F }_q}\) , a fixed algebraic closure of \(\mathbb{F }_q\) . The objective of this paper is to introduce \(J\) -invariants for a lattice of arbitrary rank. Theses \(J\) -invariants classify lattices by isomorphism. Next, we define singular lattices that are similar to classical lattices with complex multiplication. Then, we establish a result for the modular field, which is generated by the values of the \(J\) -invariants of a given singular lattice.