Forms in many variables and differing degrees
Tim D. Browning
University of Bristol, UKDavid Rodney Heath-Brown
Oxford University, UK
![Forms in many variables and differing degrees cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jems-volume-19-issue-2.png&w=3840&q=90)
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 variety , provided only that its dimension is large enough in terms of its degree.
Cite this article
Tim D. Browning, David Rodney Heath-Brown, Forms in many variables and differing degrees. J. Eur. Math. Soc. 19 (2017), no. 2, pp. 357–394
DOI 10.4171/JEMS/668