Can anyone tell me what the Ranicki symmetric L-groups $L^*(F)$ are when $F$ is a finite field? (and maybe provide a reference?) Thanks!
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$\begingroup$ This is a question which interests me a lot! $\endgroup$– Daniel MoskovichCommented Dec 5, 2010 at 0:17
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1$\begingroup$ Hi Greg, i retagged this to what I thought you meant. As it stood, this question seemed to be the only one with those tags. $\endgroup$– Sean TilsonCommented Dec 5, 2010 at 1:35
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1 Answer
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The symmetric $L$-group $L^*(F)$ of a field $F$ are 4-periodic, $$L^n(F)=L^{n+4}(F)$$ by Proposition 7.1 of http://www.maths.ed.ac.uk/~aar/papers/ats1.pdf
$L^{2i}(F)$ is the Witt group of $(-)^i$-symmetric forms: see Milnor and Husemoller!
$L^{2i+1}(F)=0$, see http://www.maths.ed.ac.uk/~aar/papers/simple.pdf (my shortest paper).
answered Dec 5, 2010 at 12:06