Counting Rational Points on Cubic Hypersurfaces

نویسنده

  • T. D. BROWNING
چکیده

Let X ⊂ P be a geometrically integral cubic hypersurface defined over Q, with singular locus of dimension 6 dimX − 4. Then the main result in this paper is a proof of the fact that X(Q) contains Oε,X(B ) points of height at most B.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Looking for Rational Curves on Cubic Hypersurfaces

The aim of these lectures is to study rational points and rational curves on varieties, mainly over finite fields Fq. We concentrate on hypersurfaces Xn of degree ≤ n+ 1 in Pn+1, especially on cubic hypersurfaces. The theorem of Chevalley–Warning (cf. Esnault’s lectures) guarantees rational points on low degree hypersurfaces over finite fields. That is, if X ⊂ Pn+1 is a hypersurface of degree ≤...

متن کامل

RATIONAL POINTS ON CUBIC HYPERSURFACES OVER Fq(t)

The Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field Fq(t), provided that char(Fq) > 3 and X has dimension at least 6.

متن کامل

Rational Points on Intersections of Cubic and Quadric Hypersurfaces

We investigate the Hasse principle for complete intersections cut out by a quadric and cubic hypersurface defined over the rational numbers.

متن کامل

Counting Rational Points on Cubic Hypersurfaces: Corrigendum

R0<b162R0 gcd(b1, N )1/2 R 0 (HP) . The second line is false and in fact one has M1 = 1 in Proposition 3. The author is very grateful to Professor Hongze Li for drawing his attention to this flaw. The error can be fixed by introducing an average over b1 into the statement of Proposition 3. This allows us to recover the main theorem in [1], and also [2, Lemma 11], via the following modification....

متن کامل

Rational Points on Cubic Hypersurfaces That Split off a Form

— Let X be a projective cubic hypersurface of dimension 11 or more, which is defined over Q. We show that X(Q) is non-empty provided that the cubic form defining X can be written as the sum of two forms that share no common variables.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008