Publication Details
Title: Aspects of Algebraic Geometry over Non Algebraically Closed Fields
Author: T. Sander
Group: ICSI Technical Reports
Date: December 1996
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1996/tr-96-055.pdf
Overview:
In this paper we study algebraic-geometric properties of the set of K-rational points V(K) of K-varieties V. We introduce an elementary class of fields K of characteristic 0 for which we prove: 1) Algebraic-geometric data of V(K) (e.g. the dimension of V(K)) can be computed under natural assumptions on K, 2) Uniform Finiteness Theorems (of Bezout Theorem type) and other complexity results and bounds, 3) Algebraic-geometric concepts are definable by first order formulas in the language of rings. This class K contains for example algebraically and real closed fields, Henselian fields (e.g. the Qp numbers and power series fields), PAC-fields (i.e. pseudo algebraically closed fields), PRC-fields and PpC-fields (of characteristic 0). Further structural properties of K are studied.
Bibliographic Information:
ICSI Technical Report TR-96-055
Bibliographic Reference:
T. Sander. Aspects of Algebraic Geometry over Non Algebraically Closed Fields. ICSI Technical Report TR-96-055, December 1996
Author: T. Sander
Group: ICSI Technical Reports
Date: December 1996
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1996/tr-96-055.pdf
Overview:
In this paper we study algebraic-geometric properties of the set of K-rational points V(K) of K-varieties V. We introduce an elementary class of fields K of characteristic 0 for which we prove: 1) Algebraic-geometric data of V(K) (e.g. the dimension of V(K)) can be computed under natural assumptions on K, 2) Uniform Finiteness Theorems (of Bezout Theorem type) and other complexity results and bounds, 3) Algebraic-geometric concepts are definable by first order formulas in the language of rings. This class K contains for example algebraically and real closed fields, Henselian fields (e.g. the Qp numbers and power series fields), PAC-fields (i.e. pseudo algebraically closed fields), PRC-fields and PpC-fields (of characteristic 0). Further structural properties of K are studied.
Bibliographic Information:
ICSI Technical Report TR-96-055
Bibliographic Reference:
T. Sander. Aspects of Algebraic Geometry over Non Algebraically Closed Fields. ICSI Technical Report TR-96-055, December 1996