We show that Diophantine problem (otherwise known as Hilbert's Tenth Problem) is undecidable over the fields of algebraic functions over the finite fields of constants of characteristic greater than two. This is the first example of Diophantine undecidability over any algebraic field. We also show t
Realization of finite groups over function fields
โ Scribed by Moshe Jarden
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 284 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
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Let V denote a finite-dimensional K vector space and let G denote a finite group of K-linear automorphisms of V. Let V m denote the direct sum of m copies of V and let G act on the symmetric algebra K[V m ] of V m by the diagonal action on V m . A result of Noether implies that, if char K=0, then K[
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Minimal sets of generators of the orthogonal groups on nonsingular quadratic spaces over a finite field are studied. All such orthogonal groups are shown to be generated by two elements, with the possible exception of two low-dimensional cases. 1994 Academic Press, Inc.