On algebraic -groups
Authors:
Piotr Kowalski and Anand Pillay
Journal:
Trans. Amer. Math. Soc. 359 (2007), 1325-1337
MSC (2000):
Primary 14K12
DOI:
https://doi.org/10.1090/S0002-9947-06-04312-1
Published electronically:
October 17, 2006
MathSciNet review:
2262852
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We introduce the categories of algebraic -varieties and
-groups over a difference field
. Under a ``linearly
-closed" assumption on
we prove an isotriviality theorem for
-groups. This theorem immediately yields the key lemma in a proof of the Manin-Mumford conjecture. The present paper crucially uses ideas of Pilay and Ziegler (2003) but in a model theory free manner. The applications to Manin-Mumford are inspired by Hrushovski's work (2001) and are also closely related to papers of Pink and Roessler (2002 and 2004).
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Additional Information
Piotr Kowalski
Affiliation:
Department of Mathematics, University of Wroclaw, pl Grunwaldzki 2/4, 50-384 Wroclaw, Poland – and – Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-2975
Anand Pillay
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-2975 – and – School of Mathematics, University of Leeds, Leeds, England LS2 9JT
DOI:
https://doi.org/10.1090/S0002-9947-06-04312-1
Received by editor(s):
January 28, 2005
Published electronically:
October 17, 2006
Additional Notes:
The first author was supported by funds from NSF Focused Research Grant DMS 01-00979, and by the Polish KBN grant 2 P03A 018 24
The second author was supported by NSF grants
Article copyright:
© Copyright 2006
American Mathematical Society