Wiki source code of MODEL THEORY OF FINITE AND PSEUDO-FINITE FIELDS 22.4.-29.4.
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1 | = MODEL THEORY OF FINITE AND PSEUDO-FINITE FIELDS = | ||
2 | |||
3 | === Intensive course === | ||
4 | |||
5 | The course is part of the activities of the graduate school MALJA. | ||
6 | |||
7 | === Lecturer === | ||
8 | |||
9 | Zoe Chatzidakis (Université Paris 7) | ||
10 | |||
11 | === Lectures === | ||
12 | |||
13 | Lectures take place in University of Helsinki, the Exactum building: | ||
14 | |||
15 | Wed, 22 Apr in C124 at 12-14 | ||
16 | Thu, 23 Apr in B322 at 12-14 | ||
17 | Fri, 24 Apr in B322 at 13-15 | ||
18 | |||
19 | Mon, 27 Apr in B322 at 12-14 | ||
20 | Tue, 28 Apr in B322 at 12-14 | ||
21 | Wed, 29 Apr in C124 at 12-14 | ||
22 | |||
23 | === Course description === | ||
24 | |||
25 | This course will study the elementary theory of finite fields, that is, | ||
26 | the set of sentences which are true in all finite fields. This theory | ||
27 | was described by Ax, and its infinite models are called pseudo-finite | ||
28 | fields. It is a decidable theory. The behaviour of pseudo-finite fields | ||
29 | gives you asymptotic information on the behaviour of finite fields, and | ||
30 | for this reason they are interesting. They are also easier to study. | ||
31 | |||
32 | We will first start by studying finite fields, and state the classical | ||
33 | theorems of Lang-Weil and of Tchebotarev. They are the main tools in the | ||
34 | axiomatisation of pseudo-finite fields. We will also describe the | ||
35 | completions of the theory of pseudo-finite fields. The algebraic notions | ||
36 | needed in the proof will be done fairly thoroughly. There will also be a | ||
37 | set of notes which will give additional details. | ||
38 | |||
39 | If time permits, we will discuss such concepts as algebraic closure, | ||
40 | definable sets, independence theorem, ranks, and some applications to | ||
41 | algebraic groups by Hrushovski and Pillay. | ||
42 | |||
43 | === Contact === | ||
44 | |||
45 | For financial support (for doctoral students of MALJA), contact | ||
46 | <Lauri.Hella AT uta.fi>. For other practical questions, contact | ||
47 | <Kerkko.Luosto AT Helsinki.FI>. |