Affine Sieve
Alireza Salehi Golsefidy, Peter Sarnak

TL;DR
This paper proves the main saturation conjecture related to applying a Brun sieve in affine linear group orbits, assuming the Zariski closure is Levi-semisimple, advancing understanding of sieve methods in algebraic group actions.
Contribution
It establishes the saturation conjecture for affine linear group orbits with Levi-semisimple Zariski closure, a significant step in sieve theory and algebraic groups.
Findings
Proves the main saturation conjecture in affine sieve setting.
Shows the Levi-semisimple condition is likely necessary.
Advances the application of Brun sieve in algebraic group orbits.
Abstract
We establish the main saturation conjecture in [BGS10] connected with executing a Brun sieve in the setting of an orbit of a group of affine linear transformations. This is carried out under the condition that the Zariski closure of the group is Levi-semisimple. It is likely that this condition is also necessary for such saturation to hold.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic Geometry and Number Theory
