Local-global principles for representations of quadratic forms
نویسندگان
چکیده
منابع مشابه
Local-global Principles for Representations of Quadratic Forms
We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension ≥ 7. The proof uses the ergodic theory of p-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.
متن کاملLocal Conditions for Global Representations of Quadratic Forms
We show that the theorem of Ellenberg and Venkatesh on representation of integral quadratic forms by integral positive definite quadratic forms is valid under weaker conditions on the represented form. In the article [5] Ellenberg and Venkatesh prove that for any integral positive definite quadratic form f in n variables there is a constant C(f) such that integral quadratic forms g of square fr...
متن کامل2 00 6 Local - Global Principles for Representations of Quadratic Forms
We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension ≥ 7. The proof uses the ergodic theory of p-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.
متن کاملApplications of quadratic D-forms to generalized quadratic forms
In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملRational Quadratic Forms and the Local-global Principle
As for most Diophantine equations, quadratic forms were first studied over the integers, meaning that the coefficients aij are integers and only integer values of x1, . . . , xn are allowed to be plugged in. At the end of the 19th century it was realized that by allowing the variables x1, . . . , xn to take rational values, one gets a much more satisfactory theory. (In fact one can study quadra...
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: Inventiones mathematicae
سال: 2007
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-007-0077-7