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


Zeta-functions 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 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.
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