Partial Hasse invariants, partial degrees and the canonical subgroup
File(s)
Accepted version
Author(s)
Bijakowski, S
Type
Journal Article
Abstract
If the Hasse invariant of a P -divisible group is small enough, then one can construct a canonical subgroup inside its P-torsion. We prove that, assuming the existence of a subgroup of adequate height in the P-torsion with high degree, the expected properties of the canonical subgroup can be easily proved, especially the relation between its degree and the Hasse invariant. When one considers a P-divisible group with an action of the ring of integers of a (possibly ramified) finite extension of QP , then much more can be said. We define partial Hasse invariants (which are natural in the unramified case, and generalize a construction of Reduzzi and Xiao in the general case), as well as partial degrees. After studying these functions, we compute the partial degrees of the canonical subgroup.
Date Issued
2018-08-01
Date Acceptance
2017-01-04
Citation
Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 2018, 70 (4), pp.742-772
ISSN
1496-4279
Publisher
Canadian Mathematical Society
Start Page
742
End Page
772
Journal / Book Title
Canadian Journal of Mathematics-Journal Canadien de Mathematiques
Volume
70
Issue
4
Copyright Statement
© 2015 The Author
Identifier
http://arxiv.org/abs/1508.07604v1
Subjects
math.NT
math.NT
Notes
29 pages, 2 tables
Publication Status
Published