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SUMMARY:Zoe Chatzidakis (CNRS - ENS)
DTSTART:20210524T080000Z
DTEND:20210524T090000Z
DTSTAMP:20260423T035614Z
UID:SiN/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/21/">A n
 ew invariant for difference fields</a>\nby Zoe Chatzidakis (CNRS - ENS) as
  part of Symmetry in Newcastle\n\n\nAbstract\nIf $(K\,f)$ is a difference 
 field\, and $a$ is a finite tuple in some difference field extending $K$\,
  and such that $f(a) \\in K(a)^{alg}$\, then we define $dd(a/K)=\\lim[K(f^
 k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. This is an inv
 ariant of the difference field extension $K(a)^{alg}/K$. We show that ther
 e is some $b$ in the difference field generated by $a$ over $K$\, which is
  equi-algebraic with $a$ over $K$\, and such that $dd(a/K)=[K(f(b)\,b):K(b
 )]$\, i.e.: for every $k>0$\, $f(b) \\in K(b\,f^k(b))$.\n\nViewing $\\math
 op{Aut}(K(a)^{alg}/K)$ as a locally compact group\, this result is connect
 ed to results of Goerge Willis on scales of automorphisms of locally compa
 ct totally disconnected groups. I will explicit the correspondence between
  the two sets of results.\n(Joint with E. Hrushovski)\n
LOCATION:https://researchseminars.org/talk/SiN/21/
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