250092 VO Algebraic Geometry (2015S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Details

Language: English

Examination dates

Lecturers

Joachim Mahnkopf

Classes (iCal) - next class is marked with N

Monday 02.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 09.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 16.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 23.03. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 13.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 20.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 27.04. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 04.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 11.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 18.05. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 01.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 08.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 15.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 22.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock
Monday 29.06. 11:30 - 13:00 Seminarraum 8 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The subject of the lecture course is a $p$-adic analogon of the spectral theory for compact operators. This analogoue was introduced by J.-P. Serre in order to explain an essential part of Dwork's proof of the rationality of the Zeta function of a variety over a finite field. Its main theorem is an anlogoue
of the Riesz theory for compact operators for completely continuous operators on $p$-adic Banach spaces. An important example of a compact operator is the Frobenius operator acting on a certain infinte dimensional space of $p$-adic power series; its characteristic series essentially equals the Zeta function.

In the lecture course we will start from basic notions of $p$-adic Banach spaces and want to present the main theorem of $p$-adic spectral theory of compact operators. Also we would like to present the application within the proof of analytic continuation and functional equation of
the Zeta function of varieties over finite fields.

Prerequisites are knowledge of basic notions of topology (mtric spaces); knowledge of $p$-adic numbers and fields ($Z_p$, $Q_p$) might be helpful but is not necessary.

Assessment and permitted materials

Oral examination

Minimum requirements and assessment criteria

Examination topics

lecture course

Reading list

Will be announced in the lecture course

Association in the course directory

MALV, MGEV

Last modified: Mo 07.09.2020 15:40