On the Hasse principle for finite group schemes over global function fields
Journal
Mathematical Research Letters
Journal Volume
19
Journal Issue
2
Pages
453-460
Date Issued
2012
Author(s)
Gonz?lez-Avil?s, C.D.
Abstract
Let K be a global function field of characteristic p > 0 and let M be a (commutative) finite and flat K-group scheme. We show that the kernel of the canonical localization map H 1 (K, M ) - all v H 1 (K v , M) in flat (fppf) cohomology can be computed solely in terms of Galois cohomology. We then give applications to the case where M is the kernel of multiplication by p m on an abelian variety defined over K.
Type
journal article