Cleanness and log-characteristic cycles, I: vector bundles with flat connections

Details Cleanness and log-characteristic cycles, I: vector bundles with flat connections Cleanness and log-characteristic cycles, I: vector bundles with flat connections

2011-04-07

arxiv.org/abs/1104.1224v1

Mathematics

Algebraic Geometry

Scientific paper

Let $X$ be a proper smooth algebraic variety over a field $k$ of characteristic zero and let $D$ be a divisor with strict simple normal crossings. For $M$ a vector bundle over $X-D$ with a flat connection having possible irregular singularities along $D$, we define a cleanness condition which says that the singularities are controlled by the ones along the generic points of $D$. When this condition is satisfied, we compute explicitly the associated logarithmic characteristic cycle. 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.

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