p-adic regulators and special values of L-functions

• Applicant: Dr. Georg Tamme
• Subject Area: Mathematics
• Term: from 2010 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 190980540

One of the deepest problems in number theory is the description of special values of L-functions. Euler already discovered a surprising formula for the value of the Riemann zeta function at the integer 2. Here 2 is a so called critical place. The study of special L-values motivated the development of many new methods in number theory and arithmetic geometry and led to a number of conjectures. For instance Bloch and Kato (for classical L-functions) and Perrin-Riou (for p-adic L- functions) describe values of L-functions (analytical objects) at integers in terms of arithmetic invariants. At the non critical places regulators play a decisive role and one may expect that a deeper study of regulator maps will lead to insights which may contribute to proofs of the above conjectures. So far, Karoubi`s approach to regulators which works equally well in the archimedean and non archimedean case has rarely been studied. After the connection to Beilinson`s regulator and to the p-adic Borel regulator has been clarified in my thesis the p-adic version of Karoubi`s regulator shall now be studied further and the relation to Perrin-Riou`s logarithm on the one hand and to Fukaya`s K2 Coleman power series on the other hand shall be investigated. It is expected that this will provide a better conceptual understanding of regulators and in the long term new insights on special values of L-functions.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Matthias Flach