کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587620 1334151 2008 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Tori and essential dimension
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Tori and essential dimension
چکیده انگلیسی

The present paper deals with algebraic tori and essential dimension in three unrelated contexts. After some preliminaries on essential dimension, versal torsors and tori, we explicitly construct a versal torsor for PGLn, n⩾5 odd, defined over a field of transcendence degree over the base field. This recovers a result of Lorenz, Reichstein, Rowen and Saltman. We also discuss the so-called “tori method” which gives a geometric proof of a result of Ledet on the essential dimension of a cyclic p-group. In the last section we compute the essential dimension of the functor K↦H1(K,GLn(Z)), the latter set being in bijection with the isomorphism classes of n-dimensional K-tori.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 319, Issue 9, 1 May 2008, Pages 3885-3900