Let be a field, a variety with tame quotient singularities, and a resolution of singularities. Any smooth rational point lifts to by the Lang-Nishimura theorem, but if is singular this might be false. For certain types of singularities, the rational point is guaranteed to lift, though; these are called singularities of type. This concept has applications in the study of the fields of moduli of varieties and yields an enhanced version of the Lang-Nishimura theorem where the smoothness assumption is relaxed. We classify completely the tame quotient singularities of type in dimension; in particular, we show that every non-cyclic tame quotient singularity in dimension is of type, and most cyclic singularities are of type too.
The Arithmetic of Tame Quotient Singularities in Dimension 2
BRESCIANI, GIULIO
2024
Abstract
Let be a field, a variety with tame quotient singularities, and a resolution of singularities. Any smooth rational point lifts to by the Lang-Nishimura theorem, but if is singular this might be false. For certain types of singularities, the rational point is guaranteed to lift, though; these are called singularities of type. This concept has applications in the study of the fields of moduli of varieties and yields an enhanced version of the Lang-Nishimura theorem where the smoothness assumption is relaxed. We classify completely the tame quotient singularities of type in dimension; in particular, we show that every non-cyclic tame quotient singularity in dimension is of type, and most cyclic singularities are of type too.File | Dimensione | Formato | |
---|---|---|---|
Bresciani - The arithmetic of tame quotient singularities in dimension 2.pdf
Accesso chiuso
Tipologia:
Published version
Licenza:
Non pubblico
Dimensione
337.56 kB
Formato
Adobe PDF
|
337.56 kB | Adobe PDF | Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.