Linear forms in zeta values and mixed Tate motives

Linear forms in zeta values and mixed Tate motives
Abstract: In order to study the diophantine properties of the values of the Riemann zeta functions
at integers, one often needs to produce integrals that evaluate to linear forms in zeta values with
rational coefficients. This is in particular the case in Beukers’s proof of Apéry’s theorem on zeta(3)
or in Ball and Rivoal’s proof that infinitely many odd zeta values are irrational. In this talk, we will
follow a program initiated by Brown which aims at explaining and producing such linear forms by
means of algebraic geometry. More precisely, we will study a family of mixed Tate motives which
underlies a family of integrals generalizing Ball and Rivoal's. In particular, the explicit computation
of their period matrices gives integral formulas for the coefficients of the linear forms.