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### Jan Dobrowolski: Sets, groups, and fields definable in vector spaces with a bilinear form

##### Donnerstag, 29.10.2020 10:30 im Raum SRZ 216/217

We study dimension, definable groups, and definable fields in vector spaces over algebraically closed [respectively, real closed] fields equipped with a non-degenerate alternating bilinear form or a non-degenerate [positive-definite] symmetric bilinear form. After a brief overview of the background, I will discuss a notion of dimension and some other ingredients of the proof of the main result, which states that, in the above context, every definable group is (algebraic-by-abelian)-by-algebraic [(semialgebraic-by-abelian)-by-semialgebraic]. It follows from this result that every definable field is definable in the field of scalars, hence either finite or definably isomorphic to it [finite or algebraically closed or real closed]

Angelegt am Freitag, 02.10.2020 10:22 von pfeifer
Geändert am Donnerstag, 15.10.2020 12:22 von pfeifer
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