Etale cohomology and weil conjecture

Abstract

In this paper, basic theory of etale cohomology on varieties and schemes (mostly on varieties) is discussed and proof of most part of Weil conjecture is given. First, we start from motivation and definition of Grothendieck topology. Then, definition and basic properties of etale cohomology of varieties and schemes are discussed. Finally, we state and discuss main theorems on etale cohomology theory and prove Weil conjecture, except Riemann hypotheses and some part of integrality, using them.