Perlen-Kolloquium: Jean-Philippe Furter (Université de la Rochelle / Basel)

Towards a theory of ind-groups? Presentation of a few ind-groups

Many groups  naturally appearing in mathematics are infinite-dimensional. This is for example (generally) the case for the automorphism group and the birational transformation group of an affine variety.

Is it possible to endow such groups with an infinite-dimensional algebraic group (for short: ind-group) structure? Can one endow such groups with a topology making them topological groups?

Finally, can one hope to develop a theory of ind-groups generalizing in some sense the well established theory of algebraic groups?

I will try to present this subject by explaining some of the involved notions. I will consider different examples, among which the n-th Cremona group.

This latter group is nothing else than the ground field fixing automorphism group of the field of rational functions in n indeterminates.

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