Prolongement de biextensions et accouplements en cohomologie log plate

Details Prolongement de biextensions et accouplements en cohomologie log plate Prolongement de biextensions et accouplements en cohomologie log plate

2009-01-31

arxiv.org/abs/0902.0081v2

International Mathematics Research Notices 2009 (2009), 3417-3444

Mathematics

Algebraic Geometry

24 pages, LaTeX. Minor changes. Numbering of items changed

Scientific paper

10.1093/imrn/rnp059

We study, using the language of log schemes, the problem of extending biextensions of smooth commutative group schemes by the multiplicative group. This was first considered by Grothendieck in SGA 7. We show that this problem admits a solution in the category of sheaves for Kato's log flat topology, in contradistinction to what can be observed using the fppf topology, for which monodromic obstructions were defined by Grothendieck. In particular, in the case of an abelian variety and its dual, it is possible to extend the Weil biextension to the whole N\'eron model. This allows us to define a pairing on the points which combines the class group pairing defined by Mazur and Tate and Grothendieck's monodromy pairing.

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