Reconstructing -divisible groups from their truncations of small level

  • Adrian Vasiu

    Binghamton University, USA


Let be an algebraically closed field of characteristic . Let be a -divisible group over . Let be the smallest non-negative integer for which the following statement holds: if is a -divisible group over of the same codimension and dimension as and such that is isomorphic to , then is isomorphic to . To the Dieudonné module of we associate a non-negative integer which is a computable upper bound of . If is a product of isoclinic -divisible groups, we show that ; if the set has at least two elements we also show that . We show that we have if and only if ; this recovers the classification of minimal -divisible groups obtained by Oort. If is quasi-special, we prove the Traverso truncation conjecture for . If is -cyclic, we explicitly compute . Many results are proved in the general context of latticed -isocrystals with a (certain) group over .

Cite this article

Adrian Vasiu, Reconstructing -divisible groups from their truncations of small level. Comment. Math. Helv. 85 (2010), no. 1, pp. 165–202

DOI 10.4171/CMH/192