

Shafarevich Seminar
November 7, 2017 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)






Zetafunctions of schemes in dimension 1 and 2
A. N. Parshin^{} ^{} Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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Abstract:
For schemes, there are two approaches to study of their
zetafunctions, 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 TateIwasawa
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.
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