Forms in many variables and differing degrees
By T. Browning, Roger Heath-Brown. 2014
62 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/047ffa03f4224e730abcb638b00b1faf6fcc3c63
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
- Emmanuel Kowalski
- Henryk Iwaniec
- P. Michel
- Kannan Soundararajan
- A. Reznikov
- Gergely Harcos
- M. Young
- V. Blomer
Citations in the corpus
- Analytic Number Theory (2021, background): “Birch’s work has been very widely generalised, for example to systems of forms with differing degrees by Browning and HeathBrown [2], to linear spaces of solutions by Brandes [3], to bihomogeneous forms by Schindler [4], and to function fields by Lee [5].”