--- res: bibo_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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Timothy D foaf_name: Browning, Timothy D foaf_surname: Browning foaf_workInfoHomepage: http://www.librecat.org/personId=35827D50-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-8314-0177 - foaf_Person: foaf_givenName: Roger foaf_name: Heath Brown, Roger foaf_surname: Heath Brown bibo_doi: 10.4171/JEMS/668 bibo_issue: '2' bibo_volume: 19 dct_date: 2017^xs_gYear dct_language: eng dct_publisher: European Mathematical Society Publishing House@ dct_title: Forms in many variables and differing degrees@ ...