David Bradley-Williams (HHU Düsseldorf): Spherically complete models of hensel minimal fields
Thursday, 23.01.2020 11:00 im Raum SR 1D
A valued field is called maximal if it admits no proper immediate extentions
(having the same residue field and value group). Krull observed that every
valued field must have some maximal immediate extension; Kaplansky established
sufficient conditions for uniqueness. In doing so, Kaplansky proved that a
field is maximal if and only if it is spherically complete: that the
intersection of any chain of closed (valuative) balls is non-empty. As can be
expected, spherical completeness can be convenient for analytic/geometric
arguments. Model theoretically, it can be helpful to transfer to a spherically
complete model, if at least one exists.
But, while every valued field has a spherically complete extension, this need
not be an elementary extension (even as a valued field). Furthermore, it
might be important to preserve extra (algebraic/analytic) structure on the
field.
Cluckers, Halupczok and Rideau have recently introduced hensel minimality for
expansions of valued fields. In this talk, we discuss the existence of
spherically complete models of hensel minimal expansions of valued fields;
joint work with Immanuel Halupczok.
Angelegt am 20.01.2020 von Martina Pfeifer
Geändert am 20.01.2020 von Martina Pfeifer
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