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SUMMARY:Zoe Chatzidakis (CNRS - ENS)
DTSTART:20210419T063000Z
DTEND:20210419T073000Z
DTSTAMP:20260423T021359Z
UID:SiN/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/16/">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 $K$\, a
 nd such that $f(a)$ in $K(a)^{alg}$\, then we define $dd(a/K)=\\mathop{lim
 }[K(f^k(a)\,a):K(a)]^{1/k}$\, the distant degree of $a$ over $K$. This is 
 an invariant of the difference field extension $K(a)^{alg}/K$. We show tha
 t there is some $b$ in the difference field generated by $a$ over $K$\, wh
 ich 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 $
 \\mathop{Aut}(K(a)^{alg}/K)$ as a locally compact group\, this result is c
 onnected to results of Goerge Willis on scales of automorphisms of locally
  compact totally disconnected groups. I will explicit the correspondence b
 etween the two sets of results.\n(Joint with E. Hrushovski)\n
LOCATION:https://researchseminars.org/talk/SiN/16/
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