Let X be a proper smooth algebraic variety over a field of characteristic zero and let be a divisor with simple normal crossings. Let be a vector bundle over equipped with a flat connection with possible irregular singularities along . We define a cleanliness condition which roughly says that the singularities of the connection are controlled by the singularities at the generic points of . When this condition is satisfied, we compute explicitly the associated log-characteristic cycle, and relate it to the so-called refined irregularities. As a corollary of a log-variant of Kashiwara-Dubson formula, we obtain the Euler characteristic of the de Rham cohomology of the vector bundle, under a mild technical hypothesis on M.
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