Tame and purely wild extensions of valued fields
نویسندگان
چکیده
منابع مشابه
Notes on extremal and Tame Valued Fields
We extend the characterization of extremal valued fields given in [1] to the missing case of valued fields of mixed characteristic with perfect residue field. This leads to a complete characterization of the tame valued fields that are extremal. The key to the proof is a model theoretic result about tame valued fields in mixed characteristic. Further, we prove that in an extremal valued field o...
متن کاملThe Algebra and Model Theory of Tame Valued Fields
A henselian valued field K is called a tame field if its algebraic closure K̃ is a tame extension, that is, the ramification field of the normal extension K̃|K is algebraically closed. Every algebraically maximal Kaplansky field is a tame field, but not conversely. We develop the algebraic theory of tame fields and then prove Ax–Kochen– Ershov Principles for tame fields. This leads to model compl...
متن کاملKummer subfields of tame division algebras over Henselian valued fields
By generalizing the method used by Tignol and Amitsur in [TA85], we determine necessary and sufficient conditions for an arbitrary tame central division algebra D over a Henselian valued field E to have Kummer subfields [Corollary 2.11 and Corollary 2.12]. We prove also that if D is a tame semiramified division algebra of prime power degree p over E such that p 6= char(Ē) and rk(ΓD/ΓF ) ≥ 3 [re...
متن کاملTame and wild kernels of quadratic imaginary number fields
For all quadratic imaginary number fields F of discriminant d > −5000, we give the conjectural value of the order of Milnor’s group (the tame kernel) K2OF , where OF is the ring of integers of F. Assuming that the order is correct, we determine the structure of the group K2OF and of its subgroup WF (the wild kernel). It turns out that the odd part of the tame kernel is cyclic (with one exceptio...
متن کاملMaximal Immediate Extensions of Valued Differential Fields
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: St. Petersburg Mathematical Journal
سال: 2008
ISSN: 1061-0022
DOI: 10.1090/s1061-0022-08-01019-4