2004/11/24 by Yves André, André, Yves, Francesco Baldassarri +1
Mathematics · #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AG #math.AP
paper · pdf · doi:10.48550/arxiv.math/0411549
N. Tsuzuki kindly indicated to us a serious error in section 2 of this paper. We think we know a way out, and are working to a revision. Please ignore this manuscript meanwhile!
arxiv created 2005/01/10 · arxiv updated 2009/12/01
Deligne's regularity criterion for an integrable connection ∇ on a smooth complex algebraic variety X says that ∇ is regular along the irreducible divisors at infinity in some fixed normal compactification of X if and only if the restriction of ∇ to every smooth curve on X is regular (\it i. e. has only regular singularities at infinity). The ``only if" part is the difficult implication. Deligne's proof is transcendental, and uses Hironaka's resolution of singularities. We give here an elementary and purely algebraic proof of this implication: it is, as far as we know, the first algebraic proof of Deligne's regularity criterion.