## The exactness of the log homotopy sequence.(English)Zbl 1180.14013

The author develops the theory of log homotopy exact sequences associated to proper log smooth morphisms and to morphisms whose characteristic sheaves are locally constant with stalks isomorphic to the monoid $$\mathbb{N}$$. To this end, a logarithmic version of the Stein factorization theorem is obtained, as well as results on the algebraization of log formal scheme.

### MSC:

 14F35 Homotopy theory and fundamental groups in algebraic geometry 14B20 Formal neighborhoods in algebraic geometry

### Keywords:

log scheme; fundamental group; log homotopy sequence.