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About: Grothendieck–Ogg–Shafarevich formula     Goto   Sponge   NotDistinct   Permalink

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Type: Thingyago:Abstraction100002137yago:Assortment108398773yago:Attribute100024264yago:Collection107951464yago:Curve113867641yago:Group100031264yago:Line113863771yago:Shape100027807yago:WikicatAbelianVarietiesyago:WikicatEllipticCurves New Facet based on Instances of this Class

In mathematics, the Grothendieck–Ogg–Shafarevich formula describes the Euler characteristic of a complete curve with coefficients in an abelian variety or constructible sheaf, in terms of local data involving the Swan conductor. Andrew Ogg and Igor Shafarevich proved the formula for abelian varieties with tame ramification over curves, and Alexander Grothendieck extended the formula to constructible sheaves over a curve.