Forms in many variables and differing degrees
Number Theory
2015-02-03 v2 Algebraic Geometry
Abstract
We generalise Birch's seminal work on forms in many variables to handle a system of forms in which the degrees need not all be the same. This allows us to prove the Hasse principle, weak approximation, and the Manin-Peyre conjecture for a smooth and geometrically integral projective variety, provided only that its dimension is large enough in terms of its degree.
Cite
@article{arxiv.1403.5937,
title = {Forms in many variables and differing degrees},
author = {T. D. Browning and D. R. Heath-Brown},
journal= {arXiv preprint arXiv:1403.5937},
year = {2015}
}
Comments
44 pages; Lemma 8.2 corrected