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Log structures, semistable degenerations, log crystalline cohomology, log de Rham cohomology, log smoothness, log Gromov-Witten theory
8
votes
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 …
4
votes
Accepted
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 …