BIBCYT Titulo: Alejandría BE 7.0.7b0

Título: =Transcendental lattices and supersingular reduction lattices of a singular K3 surface

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Autor:	Shimada, Ichiro
Título:	Transcendental lattices and supersingular reduction lattices of a singular K3 surface
Páginas/Colación:	pp. 909-949
Fecha:	February 2009

Transactions of the American Mathematical Society Vol. 361, no. 2 February 2009

Información de existencia

Resumen
A surface defined over a field of characteristic 0 is called singular if the Néron-Severi lattice of is of rank

A surface defined over a field of characteristic 0 is called singular if the Néron-Severi lattice $\mathrm{NS}(X)$ of $X\otimes \overline{k}$ is of rank . Let be a singular surface defined over a number field . For each embedding $\sigma: F\hookrightarrow \mathbb{C}$ , we denote by $T(X^\sigma)$ the transcendental lattice of the complex surface $X^\sigma$ obtained from by $\sigma$ . For each prime $\mathfrak{p}$ of at which has a supersingular reduction $X_{\mathfrak{p}}$ , we define $L(X, \mathfrak{p})$ to be the orthogonal complement of $\mathrm{NS}(X)$ in $\mathrm{NS}(X_{\mathfrak{p}})$ . We investigate the relation between these lattices $T(X\sp\sigma)$ and $L(X,\mathfrak{p})$ . As an application, we give a lower bound for the degree of a number field over which a singular surface with a given transcendental lattice can be defined.

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

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