Prolongement de biextensions et accouplements en cohomologie log plate - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: We study, using the language of log schemes, the problem of extendingbiextensions of smooth commutative group schemes by the multiplicative group.This was first considered by Grothendieck in SGA 7. We show that this problemadmits a solution in the category of sheaves for Kato-s log flat topology, incontradistinction to what can be observed using the fppf topology, for whichmonodromic obstructions were defined by Grothendieck. In particular, in thecase of an abelian variety and its dual, it is possible to extend the Weilbiextension to the whole N\-eron model. This allows us to define a pairing onthe points which combines the class group pairing defined by Mazur and Tate andGrothendieck-s monodromy pairing.



Author: Jean Gillibert

Source: https://arxiv.org/



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