Simple Complex Tori of Algebraic Dimension 0

Tatiana Bandman; Yuri G. Zarhin

doi:10.1134/S0081543823010029

Simple Complex Tori of Algebraic Dimension 0

Tatiana Bandman
, Yuri G. Zarhin

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 (US)
Pages (from-to)	21-38
Number of pages	18
Journal	Proceedings of the Steklov Institute of Mathematics
Volume	320
Issue number	1
DOIs	https://doi.org/10.1134/S0081543823010029
State	Published - Mar 2023

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

Access to Document

10.1134/S0081543823010029

Cite this

@article{d783367435ad44db86650c0a30738448,

title = "Simple Complex Tori of Algebraic Dimension 0",

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.",

author = "Tatiana Bandman and Zarhin, \{Yuri G.\}",

note = "Funding Information: This work was completed in January–May 2022 during the stay of the second author at the Max-Planck-Institut f{\"u}r 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. Funding Information: The second author was partially supported by the Simons Foundation Collaboration Grant no. 585711. Publisher Copyright: {\textcopyright} 2023, Pleiades Publishing, Ltd.",

year = "2023",

month = mar,

doi = "10.1134/S0081543823010029",

language = "English (US)",

volume = "320",

pages = "21--38",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

publisher = "Pleiades Publishing",

number = "1",

}

TY - JOUR

T1 - Simple Complex Tori of Algebraic Dimension 0

AU - Bandman, Tatiana

AU - Zarhin, Yuri G.

N1 - Funding Information: 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. Funding Information: The second author was partially supported by the Simons Foundation Collaboration Grant no. 585711. Publisher Copyright: © 2023, Pleiades Publishing, Ltd.

PY - 2023/3

Y1 - 2023/3

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85152536920

UR - https://www.scopus.com/pages/publications/85152536920#tab=citedBy

U2 - 10.1134/S0081543823010029

DO - 10.1134/S0081543823010029

M3 - Article

AN - SCOPUS:85152536920

SN - 0081-5438

VL - 320

SP - 21

EP - 38

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

IS - 1

ER -

Simple Complex Tori of Algebraic Dimension 0

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this