On Bias and Rank

17 Aug 2018  ·  Kazhdan David, Schlank Tomer M. ·

Given a hypersurface $X\subset \mathbb{P}^{N+1}_{\mathbb{C}}$ Dimca gave a proof showing that the cohomologies of X are the same as the projective space in a range determined by the dimension of the singular locus of X. We prove the analog of Dimca's result case when $\mathbb{C}$ is replaced with an algebraically closed field of finite characteristic and singular cohomology is replaced with $\ell$-adic \'etale cohomology... The Weil conjectures allow relating results about \'eatle cohomology to counting problems over a finite field. Thus by applying this result, we are able to get a relationship between the algebraic properties of certain polynomials and the size of their zero set. read more

PDF Abstract
No code implementations yet. Submit your code now

Categories


Algebraic Geometry Combinatorics