216 research outputs found
Locally Equivalent Correspondences
Given a pair of number fields with isomorphic rings of adeles, we construct
bijections between objects associated to the pair. For instance we construct an
isomorphism of Brauer groups that commutes with restriction. We additionally
construct bijections between central simple algebras, maximal orders, various
Galois cohomology sets, and commensurability classes of arithmetic lattices in
simple, inner algebraic groups. We show that under certain conditions, lattices
corresponding to one another under our bijections have the same covolume and
pro-congruence completion. We also make effective a finiteness result of Prasad
and Rapinchuk.Comment: Final Version. To appear in Ann. Inst. Fourie
Reduced group schemes as iterative differential Galois groups
This article is on the inverse Galois problem in Galois theory of linear
iterative differential equations in positive characteristic. We show that it
has an affirmative answer for reduced algebraic group schemes over any
iterative differential field which is finitely generated over its algebraically
closed field of constants. We also introduce the notion of equivalence of
iterative derivations on a given field - a condition which implies that the
inverse Galois problem over equivalent iterative derivations are equivalent.Comment: 13 page
T-motives
Considering a (co)homology theory on a base category
as a fragment of a first-order logical theory we here construct
an abelian category which is universal with respect
to models of in abelian categories. Under mild conditions on the
base category , e.g. for the category of algebraic schemes, we get
a functor from to
the category of chain complexes of ind-objects of .
This functor lifts Nori's motivic functor for algebraic schemes defined over a
subfield of the complex numbers. Furthermore, we construct a triangulated
functor from to Voevodsky's motivic
complexes.Comment: Added reference to arXiv:1604.00153 [math.AG
The p-adic monodromy theorem in the imperfect residue field case
Let K be a complete discrete valuation field of mixed characteristic (0,p)
and G_K the absolute Galois group of K. In this paper, we will prove the p-adic
monodromy theorem for p-adic representations of G_K without any assumption on
the residue field of K, for example the finiteness of a p-basis of the residue
field of K. The main point of the proof is a construction of (phi,G_K)-module
Nrig^+(V) for a de Rham representation V, which is a generalization of Pierre
Colmez' Nrig^+(V). In particular, our proof is essentially different from
Kazuma Morita's proof in the case when the residue field admits a finite
p-basis.
We also give a few applications of the p-adic monodromy theorem, which are
not mentioned in the literature. First, we prove a horizontal analogue of the
p-adic monodromy theorem. Secondly, we prove an equivalence of categories
between the category of horizontal de Rham representations of G_K and the
category of de Rham representations of an absolute Galois group of the
canonical subfield of K. Finally, we compute H^1 of some p-adic representations
of G_K, which is a generalization of Osamu Hyodo's results.Comment: 41 page
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