# Introduction, main results, context

# Introduction, main results, context

This chapter provides an introduction to the subject, precise statements of the main results, and places these in a somewhat wider context. Topics discussed include statement of the main results, Schoof's algorithm, Schoof's algorithm described in terms of ètale cohomology, other cases where ètale cohomology can be used to construct polynomial time algorithms for counting rational points of varieties over finite fields, congruences for Ramanujan's tau-function, and comparison with p-adic methods.

*Keywords:*
modular forms, Schoof's algorithm, Ramanujan's tau-function, ètale cohomology, polynomial time algoriths, p-adic methods

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