This paper studies the CBP, a model-theoretic property first discovered by Pillay and Ziegler. We first show a general decomposition result of the types of canonical bases, which one can think of as a sort of primary decomposition. This decomposition is then used to show that existentially closed difference fields of any characteristic have the CBP. We also derive consequences of the CBP, and use these results for applications to differential and difference varieties, and algebraic dynamics.
@article{CML_2012__4_3_A2_0,
author = {Chatzidakis, Zo\'e},
title = {A note on canonical bases and one-based types in supersimple theories},
journal = {Confluentes Mathematici},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {4},
number = {3},
year = {2012},
doi = {10.1142/S1793744212500041},
language = {en},
url = {http://archive.numdam.org/articles/10.1142/S1793744212500041/}
}
TY - JOUR AU - Chatzidakis, Zoé TI - A note on canonical bases and one-based types in supersimple theories JO - Confluentes Mathematici PY - 2012 VL - 4 IS - 3 PB - World Scientific Publishing Co Pte Ltd UR - http://archive.numdam.org/articles/10.1142/S1793744212500041/ DO - 10.1142/S1793744212500041 LA - en ID - CML_2012__4_3_A2_0 ER -
%0 Journal Article %A Chatzidakis, Zoé %T A note on canonical bases and one-based types in supersimple theories %J Confluentes Mathematici %D 2012 %V 4 %N 3 %I World Scientific Publishing Co Pte Ltd %U http://archive.numdam.org/articles/10.1142/S1793744212500041/ %R 10.1142/S1793744212500041 %G en %F CML_2012__4_3_A2_0
Chatzidakis, Zoé. A note on canonical bases and one-based types in supersimple theories. Confluentes Mathematici, Tome 4 (2012) no. 3. doi : 10.1142/S1793744212500041. http://archive.numdam.org/articles/10.1142/S1793744212500041/
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