Forms in many variables and differing degrees

2014/03/24 by Browning, T. D., Heath-Brown, D. R. · 1 citation
#11G35 (11P55 #14G05) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1403.5937

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 projective variety, provided only that its dimension is large enough in terms of its degree.

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• Polynomial Bounds for Birch's Theorem

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