113 research outputs found
Finiteness Theorems for Deformations of Complexes
We consider deformations of bounded complexes of modules for a profinite
group G over a field of positive characteristic. We prove a finiteness theorem
which provides some sufficient conditions for the versal deformation of such a
complex to be represented by a complex of G-modules that is strictly perfect
over the associated versal deformation ring.Comment: 25 pages. This paper is connected to the paper arXiv:0901.010
Embedding Problems and Finite Quotients
We give a condition on a family of solutions of quotients of an embedding problem which implies the embedding problem has a solution. This shows, in particular, that to solve an embedding problem associated to the maximal extension of a number field unramified outside a fixed finite set of places, it suffices to find a solution for each finite quotient of the embedding problem. This statement is not true in general over global function fields, but one can prove variants of it in this case in which extra conditions on the embedding problems or on the ramification of solutions are assumed
Oort groups and lifting problems
Let k be an algebraically closed field of positive characteristic p. We
consider which finite groups G have the property that every faithful action of
G on a connected smooth projective curve over k lifts to characteristic zero.
Oort conjectured that cyclic groups have this property. We show that if a
cyclic-by-p group G has this property, then G must be either cyclic or
dihedral, with the exception of A_4 in characteristic 2. This proves one
direction of a strong form of the Oort Conjecture.Comment: 20 page
- …