Abstract:
For schemes, there are two approaches to study of their
zeta-functions, cohomological or motivic approach and adelic one. We
will study the adelic approach for the zeta -functions of schemes
which are algebraic curves or surfaces defined over a finite
field. Firstly, we consider a version of the classical Tate-Iwasawa
method for curves where we remove the well known manipulations with
formulas and replace them by functoriality and duality
considerations. Next, we discuss a possible extension of these
constructions on the case of a surface.
Series of lectures
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