Geodesic
Simple Complex Tori of Algebraic Dimension 0
Informatics and Automation, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 27-45

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Using Galois theory, we explicitly construct (in all complex dimensions $g\ge 2$) an infinite family of simple $g$-dimensional complex tori $T$ that enjoy the following properties: $\bullet $ the Picard number of $T$ is $0;$ in particular, the algebraic dimension of $T$ is $0$; $\bullet $ if $T^\vee $ is the dual of $T$, then $\mathrm {Hom}(T,T^\vee )=\{0\}$; $\bullet $ the automorphism group $\mathrm {Aut}(T)$ of $T$ is isomorphic to $\{\pm 1\} \times \mathbb Z^{g-1}$; $\bullet $ the endomorphism algebra $\mathrm {End}^0(T)$ of $T$ is a purely imaginary number field of degree $2g$.
Keywords: complex tori
Mots-clés : algebraic dimension 0. 
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     author = {Tatiana Bandman and Yuri G. Zarhin},
     title = {Simple {Complex} {Tori} of {Algebraic} {Dimension} 0},
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Tatiana Bandman; Yuri G. Zarhin. Simple Complex Tori of Algebraic Dimension 0. Informatics and Automation, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 27-45. http://geodesic.mathdoc.fr/item/TRSPY_2023_320_a1/