#
nLab

Szpiro's conjecture

A statement about elliptic curves.

## Relation to other statements

In its general form, equivalent to the abc conjecture.

If Mochizuki's corollary 3.12 is true, then Szpiro’s conjecture is also true.

## References

The relation to the abc conjecture is discussed in

- Matt Baker (notes taken by William Stein),
*Elliptic curves, the ABC conjecture, and points of small canonical height* (pdf)

The relation to Mochizuki's corollary 3.12 is discussed in

- Taylor Dupuy, Anton Hilado,
*Probabilistic Szpiro, Baby Szpiro, and Explicit Szpiro from Mochizuki’s Corollary 3.12*, (arxiv:2004.13108)