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An analogue of the Andre-Oort conjecture for products of Drinfeld modular surfaces

Karumbidza, Archie (2013-03)

Thesis (PhD)--Stellenbosch University, 2013.


ENGLISH ABSTRACT: This thesis deals with a function eld analog of the André-Oort conjecture. The (classical) André-Oort conjecture concerns the distribution of special points on Shimura varieties. In our case we consider the André-Oort conjecture for special points in the product of Drinfeld modular varieties. We in particular manage to prove the André- Oort conjecture for subvarieties in a product of two Drinfeld modular surfaces under a characteristic assumption.

AFRIKAANSE OPSOMMING: Hierdie tesis handel van 'n funksieliggaam analoog van die André-Oort Vermoeding. Die (Klassieke) André-Oort Vermoeding het betrekking tot die verspreiding van spesiale punte op Shimura varietiete. Ons geval beskou ons die André-Oort Vermoeding vir spesiale punte op die produk Drinfeldse modulvarietiete. In die besonders, bewys ons die André-Oort Vermoeding vir ondervarieteite van 'n produk van twee Drinfeldse modulvarietiete, onderhewig aan 'n karakteristiek-aanname.

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