Geodesic
Simple Complex Tori of Algebraic Dimension 0
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 27-45

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2023_320_a1,
     author = {Tatiana Bandman and Yuri G. Zarhin},
     title = {Simple {Complex} {Tori} of {Algebraic} {Dimension} 0},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {27--45},
     publisher = {mathdoc},
     volume = {320},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2023_320_a1/}
}
TY  - JOUR
AU  - Tatiana Bandman
AU  - Yuri G. Zarhin
TI  - Simple Complex Tori of Algebraic Dimension 0
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2023
SP  - 27
EP  - 45
VL  - 320
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2023_320_a1/
LA  - ru
ID  - TM_2023_320_a1
ER  - 
%0 Journal Article
%A Tatiana Bandman
%A Yuri G. Zarhin
%T Simple Complex Tori of Algebraic Dimension 0
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2023
%P 27-45
%V 320
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2023_320_a1/
%G ru
%F TM_2023_320_a1
Tatiana Bandman; Yuri G. Zarhin. Simple Complex Tori of Algebraic Dimension 0. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 27-45. http://geodesic.mathdoc.fr/item/TM_2023_320_a1/