Geodesic
Forms in many variables and differing degrees
Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 357-394

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.4171/jems/668
Classification : 11-XX, 14-XX
Keywords: Hardy-Littlewood circle method, complete intersections, Hasse principle, weak approximation, rational points, Manin conjecture, forms in many variables 
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Tim D. Browning; David Rodney Heath-Brown. Forms in many variables and differing degrees. Journal of the European Mathematical Society, Tome 19 (2017) no. 2, pp. 357-394. doi: 10.4171/jems/668

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