119 research outputs found
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
Quadratic forms and linear algebraic groups
Topics discussed at the workshop Quadratic Forms and Linear Algebraic Groups included besides the algebraic theory of quadratic and Hermitian forms and their Witt groups several aspects of the theory of linear algebraic groups and homogeneous varieties, as well as some arithmetic aspects pertaining to the theory of quadratic forms over function fields over local fields
Local-global principles for Galois cohomology
This paper proves local-global principles for Galois cohomology groups over
function fields of curves that are defined over a complete discretely
valued field. We show in particular that such principles hold for , for all . This is motivated by work of Kato and others, where
such principles were shown in related cases for . Using our results in
combination with cohomological invariants, we obtain local-global principles
for torsors and related algebraic structures over . Our arguments rely on
ideas from patching as well as the Bloch-Kato conjecture.Comment: 32 pages. Some changes of notation. Statement of Lemma 2.4.4
corrected. Lemma 3.3.2 strengthened and made a proposition. Some proofs
modified to fix or clarify specific points or to streamline the presentatio
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