Weil's Conjecture for Function Fields

A central concern of number theory is the study of local-to-global principles, which describe the behavior of a global field K in terms of the behavior of various completions of K . This book looks at a specific example of a local-to-global principle: Weil’s conjecture on the Tamagawa number of a semisimple algebraic group G over K . In the case where K is the function field of an algebraic curve X , this conjecture counts the number of G -bundles on X (global information) in terms of the reduct