A note on Galois groups of algebraic closures
نویسندگان
چکیده
منابع مشابه
On Fundamental Groups of Galois Closures of Generic Projections
We study the fundamental group of the Galois closure Xgal of a generic projection from a surface X. Originally, it was believed that π1(Xgal) gives rise to new invariants of X. However, in all examples this group is surprisingly simple. In this article, we offer an explanation for this phenomenon: We compute a quotient of π1(Xgal) that depends on π1(X) and data from the generic projection only....
متن کاملFundamental Groups of Galois Closures of Generic Projections
For the Galois closure Xgal of a generic projection from a surface X, it is believed that π1(Xgal) gives rise to new invariants of X. However, in all examples this group is surprisingly simple. In this article, we offer an explanation for this phenomenon: We compute a quotient of π1(Xgal) that depends on π1(X) and data from the generic projection only. In all known examples, this quotient is in...
متن کاملAlgebraic D-groups and Differential Galois Theory
We discuss various relationships between the algebraic Dgroups of Buium, 1992, and differential Galois theory. In the first part we give another exposition of our general differential Galois theory, which is somewhat more explicit than Pillay, 1998, and where generalized logarithmic derivatives on algebraic groups play a central role. In the second part we prove some results with a “constrained...
متن کاملA Note on the Inverse Limits of Linear Algebraic Groups
In this paper, we investigate some properties of inverse limits of linear algebraic groups. For example, we show that if G = lim ←−Gi, where (Gi, πji)i,j∈I is an inverse system of algebraic groups over an algebraically closed field. Then each canonical projection πi : G → Gi maps closed subgroups of G onto closed subgroups of Gi. Furthermore, we prove directly that the inverse limit of an inver...
متن کاملLinear algebraic groups as parameterized Picard–Vessiot Galois groups
We show that a linear algebraic group is the Galois group of a parameterized Picard-Vessiot extension of k(x), x′ = 1, for certain differential fields k, if and only if its identity component has no one dimensional quotient as a linear algebraic group.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1976
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700016864