FOR 570: Algebraic Cycles and L-functions

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The research project belongs to the intersection of number theory and algebraic geometry inside mathematics. Basic for number theory is the problem to solve algebraic equations and to make as far as possible quantitative and qualitative statements about these solutions. For this purpose, it has become useful to encode the number of solutions (over finite fields for every prime number p) in the so-called L-function. Many deep statements can be or should be read of from the properties of the L-function. We mention the Riemann conjecture and the Birch-Swinnerton-Dyer conjecture, two of the seven millennium price problems of mathematics.