Local-global Principles for Representations of Quadratic Forms
نویسنده
چکیده
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.
منابع مشابه
2 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 کاملApproximating the Distributions of Singular Quadratic Expressions and their Ratios
Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...
متن کاملGalois Representations for Holomorphic Siegel Modular Forms
We prove local global compatibility (up to a quadratic twist) of Galois representations associated to holomorphic Hilbert-Siegel modular forms in many cases (induced from Borel or Klingen parabolic). For Siegel modular forms, when the local representation is an irreducible principal series we get local global compatibility without a twist. We achieve this by proving a version of rigidity (stron...
متن کاملFiniteness results for regular ternary quadratic polynomials
In 1924, Helmut Hasse established a local-to-global principle for representations of rational quadratic forms. Unfortunately, an analogous local-to-global principle does not hold for representations over the integers. A quadratic polynomial is called regular if such a principle exists; that is, if it represents all the integers which are represented locally by the polynomial itself over Zp for ...
متن کاملAxiomatization of local-global principles for pp-formulas in spaces of orderings
Two important results in quadratic form theory, Pfister’s local-global principle and the isotropy theorem (see [5]), can be stated more generally for spaces of orderings (an abstract version of real spectras of formally real fields), for which they are expressed as local-global principles: A property of quadratic forms (expressed as a so-called positive-primitive formula) holds if and only if i...
متن کامل