Difference fields and descent of difference varieties

1 hour 2 mins 31 secs, 388.50 MB, QuickTime 384x288, 25.0 fps, 44100 Hz, 848.45 kbits/sec

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Description:	Chatzidakis, Z (Paris 7 - Denis-Diderot) Tuesday 12 May 2009, 16:30-17:30 Algebraic Theory of Difference Equations

Created:

2009-06-03 23:12

Collection:

Discrete Integrable Systems

Publisher:

Isaac Newton Institute

Chatzidakis, Z

Language:

eng (English)

Credits:

Author:	Chatzidakis, Z
Director:	Steven White


Abstract:	In this talk I will state and explain a few results of descent of difference varieties which can be obtained using model theoretic tools. The typical statement is the following: Let K_1 and K_2 be difference fields, and V_i, i=1,2, difference varieties defined over K_i. Assume that there is a dominant rational difference morphism from V_1 onto V_2. Then V_2 in turns dominates some difference variety defined over K=K_1\cap K_2. This result is of course not true as stated, and we explain which hypotheses make it valid. In particular it gives an alternate proof of a result of M. Baker on algebraic dynamics and generalises it to higher dimensions. This is joint work with Ehud Hrushovski. Extended abstract, at http://www.logique.jussieu.fr/~zoe/papiers/Leeds09.pdf

Abstract:

In this talk I will state and explain a few results of descent of difference varieties which can be obtained using model theoretic tools. The typical statement is the following: Let K_1 and K_2 be difference fields, and V_i, i=1,2, difference varieties defined over K_i. Assume that there is a dominant rational difference morphism from V_1 onto V_2. Then V_2 in turns dominates some difference variety defined over K=K_1\cap K_2. This result is of course not true as stated, and we explain which hypotheses make it valid. In particular it gives an alternate proof of a result of M. Baker on algebraic dynamics and generalises it to higher dimensions. This is joint work with Ehud Hrushovski. Extended abstract, at http://www.logique.jussieu.fr/~zoe/papiers/Leeds09.pdf

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