WEIL NUMBERS AND FORMS FOR VARIETIES OVER FINITE FIELDS.

Title: WEIL NUMBERS AND FORMS FOR VARIETIES OVER FINITE FIELDS.
Identifier: AAI8501169
identifier: 8501169
Creator: SARKISIAN, RICHARD GABRIEL.
Contributor: Ray Hoobler
Date: 1984
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: This dissertation consists of four chapters. The zeroth chapter is a review of basic facts about abelian varieties over finite fields, in particular, theorems of Tate and Honda which give a bijective correspondsence between isogeny classes of simple abelian varieties over F(,q) and conjugacy classes of q-Weil numbers. In the first chapter the question of how the corresponding isogeny class changes when a q-Weil number is multiplied by a root of unity is investigated. The answer relies upon the isogeny factorization of the "descending the ground field" or norm construction. In the second chapter an application is made to relate the roots of the L-function and zeta function of an Artin-Schreier cover of a variety over a finite field. In the third chapter it is proved that there exists a correspondence between the norm of an algebraic curve over a finite field and a product of forms for the curve.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.
Program: Mathematics