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Logarithmic structures of Fontaine-Illusie. (English) Zbl 0776.14004
Algebraic analysis, geometry, and number theory, Proc. JAMI Inaugur. Conf., Baltimore/MD (USA) 1988, 191-224 (1989).
[For the entire collection see Zbl 0747.00038.]
The author introduces the basic facts about logarithmic structures. These have been introduced to give a crystalline interpretation for logarithmic de Rham cohomology. They are not only successful in this respect, but apply to semistable varieties, and provide a new approach to torus- embeddings.

MSC:
 14F30 $$p$$-adic cohomology, crystalline cohomology 14F40 de Rham cohomology and algebraic geometry 14E25 Embeddings in algebraic geometry