Fixing X in the multiplicative algebraic group G^n_m(\Q), we are interested in the intersection of X with the union of Y where Y runs through the algebraic subgroups of G^n_m restricted only by dimension. We shall prove that, if X is an irreducible subvariety in G^n_m and the considered algebraic subgroups have codimension at least dim X, then this intersection has a bounded height by removing the anomalous sub varieties of X. Furthermore, we recover the finiteness by considering the algebraic subgroups of codimension at least 1 + dim X.

Some problems of unlikely intersections

Andriamandratomanana, Njaka Harilala
2020/2021

Abstract

Fixing X in the multiplicative algebraic group G^n_m(\Q), we are interested in the intersection of X with the union of Y where Y runs through the algebraic subgroups of G^n_m restricted only by dimension. We shall prove that, if X is an irreducible subvariety in G^n_m and the considered algebraic subgroups have codimension at least dim X, then this intersection has a bounded height by removing the anomalous sub varieties of X. Furthermore, we recover the finiteness by considering the algebraic subgroups of codimension at least 1 + dim X.
2020-07-15
46
unlikely intersection, algebraic torus
File in questo prodotto:
File Dimensione Formato  
tesi_ANDRIAMANDRATOMANANA.pdf

accesso aperto

Dimensione 758.05 kB
Formato Adobe PDF
758.05 kB Adobe PDF Visualizza/Apri

The text of this website © Università degli studi di Padova. Full Text are published under a non-exclusive license. Metadata are under a CC0 License

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/21434