We prove that a semialgebraically connected affine Nash group over a real closed field R is Nash isogenous to the semialgebraically connected component of the group H(R) of R-points of some algebraic group H defined over R. In the case when R = ℝ, this result was claimed in [5], but a mistake in the proof was recently found, and the new proof we obtained has the advantage of being valid over an arbitrary real closed field. We also extend the result to not necessarily connected affine Nash groups over arbitrary real closed fields.
@article{CML_2011__3_4_577_0,
author = {Hrushovski, Ehud and Pillay, Anand},
title = {Affine {Nash} groups over real closed fields},
journal = {Confluentes Mathematici},
pages = {577--585},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {3},
number = {4},
year = {2011},
doi = {10.1142/S179374421100045X},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S179374421100045X/}
}
TY - JOUR AU - Hrushovski, Ehud AU - Pillay, Anand TI - Affine Nash groups over real closed fields JO - Confluentes Mathematici PY - 2011 SP - 577 EP - 585 VL - 3 IS - 4 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S179374421100045X/ DO - 10.1142/S179374421100045X LA - en ID - CML_2011__3_4_577_0 ER -
%0 Journal Article %A Hrushovski, Ehud %A Pillay, Anand %T Affine Nash groups over real closed fields %J Confluentes Mathematici %D 2011 %P 577-585 %V 3 %N 4 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S179374421100045X/ %R 10.1142/S179374421100045X %G en %F CML_2011__3_4_577_0
Hrushovski, Ehud; Pillay, Anand. Affine Nash groups over real closed fields. Confluentes Mathematici, Tome 3 (2011) no. 4, pp. 577-585. doi : 10.1142/S179374421100045X. http://www.numdam.org/articles/10.1142/S179374421100045X/
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