On the Growth of Koszul Homology and Estimates of Betti Numbers of Semi-Perverse Sheaves on Pro-l Towers

Abstract

In this thesis we will prove a general version of a vanishing result of P. Scholze and H. Esnault on the cohomology of pro-l towers and relate it, via the generalized Fourier-Mellin transform, to classical growth estimates of Betti numbers of semi- perverse sheaves on pro-l towers, as posed by A. A. Beilinson. Motivated by this, we will investigate the growth of Koszul homology for powers of sequences, and we will study its interplay with dimension theory. In doing so, we will examine several aspects that, in a bigger picture, are related to questions historically associated with B ́ezout’s theorem