Group schemes of period p >2

GROUP SCHEMES OF PERIOD p > 2

For a prime number p > 2, we give a direct proof of Breuil’s classification of killed by p finite flat group schemes over the valuation ring of a p-adic field with perfect residue field. As application we prove that the Galois modules of geometric points of such group schemes and of their characteristic p analogues coming from Faltings’s strict modules can be identified via the Fontaine-Wintenb...

Group Schemes of Period 2

We give an explicit construction of the antiequivalence of the category of finite flat commutative group schemes of period 2 defined over a valuation ring of a 2-adic field with algebraically closed residue field. This result extends the earlier author’s approach to group schemes of period p > 2 from Proceedings LMS, 101, 2010, 207-259.

m at h . A G ] 1 7 Ju l 2 00 9 GROUP SCHEMES OF PERIOD p > 2

For a prime number p > 2, we give a direct proof of Breuil’s classification of finite flat group schemes killed by p over the valuation ring of a p-adic field with perfect residue field. As application we establish a correspondence between finite flat group schemes and Faltings’s strict modules which respects associated Galois modules via the Fontaine-Wintenberger field-of-norms functor

THE p-PERIODICITY OF THE MAPPING CLASS GROUP AND THE ESTIMATE OF ITS p-PERIOD

We determine completely the primes p for which the Farrell-Tate cohomology of the mapping class group Tg is /»-periodic. We also estimate the p-period of a p-periodic T„ . For T any group of finite virtual cohomological dimension (vcd) and a prime p, we say that the group Y has p-periodic cohomology if there exists a positive integer d such that the Farrell-Tate cohomology groups //'(r; M) and ...

Group Schemes