653 research outputs found
Separably closed fields and contractive Ore modules
We consider valued fields with a distinguished contractive map as valued
modules over the Ore ring of difference operators. We prove quantifier
elimination for separably closed valued fields with the Frobenius map, in the
pure module language augmented with functions yielding components for a p-basis
and a chain of subgroups indexed by the valuation group
Necklace rings and logarithmic functions
In this paper, we develop the theory of the necklace ring and the logarithmic
function. Regarding the necklace ring, we introduce the necklace ring functor
from the category of special \ld-rings into the category of special
\ld-rings and then study the associated Adams operators. As far as the
logarithmic function is concerned, we generalize the results in Bryant's paper
(J. Algebra. 253 (2002); no.1, 167-188) to the case of graded Lie
(super)algebras with a group action by applying the Euler-Poincar\'e principle
Two-point coordinate rings for GK-curves
Giulietti and Korchm\'aros presented new curves with the maximal number of
points over a field of size q^6. Garcia, G\"uneri, and Stichtenoth extended the
construction to curves that are maximal over fields of size q^2n, for odd n >=
3. The generalized GK-curves have affine equations x^q+x = y^{q+1} and
y^{q^2}-y^q = z^r, for r=(q^n+1)/(q+1). We give a new proof for the maximality
of the generalized GK-curves and we outline methods to efficiently obtain their
two-point coordinate ring.Comment: 16 page
Amalgamation of types in pseudo-algebraically closed fields and applications
This paper studies unbounded PAC fields and shows an amalgamation result for
types over algebraically closed sets. It discusses various applications, for
instance that omega-free PAC fields have the property NSOP3. It also contains a
description of imaginaries in PAC fields.Comment: Minor changes in v3. Accepted versio
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