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

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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)

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10.1134/S0081543823010029

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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",

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doi = "10.1134/S0081543823010029",

language = "English (US)",

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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.

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JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

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Simple Complex Tori of Algebraic Dimension 0

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