Geometry on totally separably closed schemes
نویسندگان
چکیده
منابع مشابه
Separably closed fields with Hasse derivations
In [6] Messmer and Wood proved quantifier elimination for separably closed fields of finite Ershov invariant e equipped with a (certain) Hasse derivation. We propose a variant of their theory, using a sequence of e commuting Hasse derivations. In contrast to [6] our Hasse derivations are iterative.
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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.
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We consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection. We prove in particular that no new definable groups arise in this way: we show that any group definable in such a field L is definably isomorphic to the group of L-rational points of an algebraic group defined over L.
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We consider separably closed fields of characteristic p > 0 and fixed Imperfection degree as modules over a skew polynomial ring. We axlotnatlze the correspondltlg theory and ue show that i t is complete and that ~t adnilts quantifier e l ~ n i ~ n a t ~ o n In the usual nlodule language augmented with additwe functions whlch are the analog of the p-component functions. $
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In Dellunde et al. (J. Symbolic Logic 67(3) (2002) 997–1015), we determined the complete theory Te of modules of separably closed %elds of characteristic p and imperfection degree e, e∈! ∪ {∞}. Here, for 0 = e∈!, we describe the closed set of the Ziegler spectrum corresponding to Te. Further, we establish a correspondence between certain submodules and n-types and we investigate several notions...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2017
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2017.11.537