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Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory

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References for logarithmic geometry

One standard reference is Luc Illusie. An overview of the work of K. Fujiwara, K. Kato, and C. Nakayama on logarithmic ́etale cohomology. Ast ́erisque, (279):271–322, 2002. Cohomologies p-adiques et …
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Logarithmic structures on moduli of elliptic curves over Z

I thing Kato's log purity theorem gives you this. See, for instance, Theorem B in Mochizuki's "Extending Families of Curves over Log Regular Schemes." I think all you need is that the cusps form a n …
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