Submission date: 15 March 2018

Abstract:

We formulate two weak versions of Pila's Modular Zilber-Pink with derivatives (MZPD) conjecture and prove them assuming a weak existential closedness conjecture for the differential equation of the j-function. Using those results we establish a weak Modular André-Oort with derivatives statement unconditionally. Then using André-Oort we give an unconditional proof for a special case of one of the aforementioned weak MZPD conjectures.

Mathematics Subject Classification:

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Full text arXiv 1803.05895: pdf, ps.