Forms in many variables and differing degrees

Tim Browning; Roger Heath-Brown

doi:10.4171/JEMS/668

Forms in many variables and differing degrees

Tim Browning, Roger Heath-Brown

Research output: Contribution to journal › Article (Academic Journal) › peer-review

27 Citations (Scopus)

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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 P^m, provided only that its dimension is large enough in terms of its degree.

Original language	English
Pages (from-to)	357-394
Number of pages	38
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/668
Publication status	Published - 26 Jan 2017

Keywords

Complete intersections
Forms in many variables
Hardy-Littlewood circle method
Hasse principle
Rational points Manin conjecture
Weak approximation

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10.4171/JEMS/668

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This is the accepted author manuscript (AAM). The final published version (version of record) is available online via EMS at http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=19&iss=2&rank=2 . Please refer to any applicable terms of use of the publisher.
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KW - Rational points Manin conjecture

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Forms in many variables and differing degrees

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Keywords

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