Forms in many variables and differing degrees

T.D. Browning, R. Heath Brown, Journal of the European Mathematical Society 19 (2017) 357–394.


Journal Article | Published
Author
Browning, Timothy DIST Austria ; Heath-Brown, Roger
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 X Pm, provided only that its dimension is large enough in terms of its degree.
Publishing Year
Date Published
2017-01-26
Journal Title
Journal of the European Mathematical Society
Acknowledgement
While working on this paper the first author was supported by ERC grant 306457.
Volume
19
Issue
2
Page
357 - 394
IST-REx-ID
266

Cite this

Browning TD, Heath Brown R. Forms in many variables and differing degrees. Journal of the European Mathematical Society. 2017;19(2):357-394. doi:10.4171/JEMS/668
Browning, T. D., & Heath Brown, R. (2017). Forms in many variables and differing degrees. Journal of the European Mathematical Society. European Mathematical Society Publishing House. https://doi.org/10.4171/JEMS/668
Browning, Timothy D, and Roger Heath Brown. “Forms in Many Variables and Differing Degrees.” Journal of the European Mathematical Society. European Mathematical Society Publishing House, 2017. https://doi.org/10.4171/JEMS/668.
T. D. Browning and R. Heath Brown, “Forms in many variables and differing degrees,” Journal of the European Mathematical Society, vol. 19, no. 2. European Mathematical Society Publishing House, pp. 357–394, 2017.
Browning TD, Heath Brown R. 2017. Forms in many variables and differing degrees. Journal of the European Mathematical Society. 19(2), 357–394.
Browning, Timothy D., and Roger Heath Brown. “Forms in Many Variables and Differing Degrees.” Journal of the European Mathematical Society, vol. 19, no. 2, European Mathematical Society Publishing House, 2017, pp. 357–94, doi:10.4171/JEMS/668.
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