Simple Complex Tori of Algebraic Dimension 0

Tatiana Bandman, Yuri G. Zarhin

Research output: Contribution to journalArticlepeer-review

Abstract

Abstract: Using Galois theory, we explicitly construct (in all complex dimensions (Formula presented.)) an infinite family of simple g-dimensional complex tori T that enjoy the following properties: (Formula presented.) the Picard number of T is 0; in particular, the algebraic dimension of T is 0; (Formula presented.) if (Formula presented.) is the dual of T, then (Formula presented.); (Formula presented.) the automorphism group (Formula presented.) of T is isomorphic to (Formula presented.); (Formula presented.) the endomorphism algebra (Formula presented.) of T is a purely imaginary number field of degree 2g.

Original languageEnglish
Pages (from-to)21-38
Number of pages18
JournalProceedings of the Steklov Institute of Mathematics
Volume320
Issue number1
DOIs
StatePublished - Mar 2023

Bibliographical note

Publisher Copyright:
© 2023, Pleiades Publishing, Ltd.

Keywords

  • algebraic dimension 0
  • complex tori

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