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 language | English |
|---|---|
| Pages (from-to) | 21-38 |
| Number of pages | 18 |
| Journal | Proceedings of the Steklov Institute of Mathematics |
| Volume | 320 |
| Issue number | 1 |
| DOIs | |
| State | Published - Mar 2023 |
Bibliographical note
Publisher Copyright:© 2023, Pleiades Publishing, Ltd.
Funding
This work was completed in January–May 2022 during the stay of the second author at the Max-Planck-Institut für Mathematik (Bonn, Germany), whose hospitality and support are gratefully acknowledged. We are also grateful to the referee, whose thoughtful comments helped to improve the exposition. The second author was partially supported by the Simons Foundation Collaboration Grant no. 585711.
| Funders | Funder number |
|---|---|
| Max-Planck-Institut für Mathematik | |
| Simons Foundation | 585711 |
Keywords
- algebraic dimension 0
- complex tori