Weronika Czerniawska: “Unifying global theory for the Riemann-Roch theorem in low dimensions”

Weronika Czerniawska: “Unifying global theory for the Riemann-Roch theorem in low dimensions”

The analogy between the theory of number fields and of function fields of curves over finite fields has been an impulse for development of geometric points of view towards arithmetic problems. In particular,in the PhD thesis of J. Tate it has been shown that harmonic analysis on one-dimensional global fields can serve as a unifying theory for the two sides of the picture.

In my talk I am going to present recently developed two-dimensional generalisation of this unifying point of view. (Joint work with P. Dolce and I. Fesenko)