Welcome to MathOverflow

Question

9

2

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!

edited Dec 5 2010 at 1:34

Sean Tilson
2,362●9●24

asked Dec 4 2010 at 23:55

Greg Friedman
2,074●4●14

This is a question which interests me a lot! – Daniel Moskovich Dec 5 2010 at 0:17

1

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. – Sean Tilson Dec 5 2010 at 1:35

thanks. I had a feeling I bungled that. – Greg Friedman Dec 5 2010 at 19:41

Andrew Ranicki · Accepted Answer · 2010-12-05 12:06:56Z UTC

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).

Ranicki symmetric L-groups of finite fields?

Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)

1 Answer

You can accept an answer to one of your own questions by clicking the check mark next to it. This awards 15 reputation points to the person who answered and 2 reputation points to you.