Arithmetische Geomterie (SS 2020)
Vorlesung
- Dienstag, 14:15-15:45 Uhr, online
- Mittwoch, 09:15-10:45 Uhr, online
- Beginn: Dienstag, 21.04.2020, 14:15 Uhr
- Die Vorlesung findet online über die Plattform Zoom statt; die entsprechenden Links sind auf der entsprechenden Moodle-Homepage zu finden
Summary of the course
Arithmetic intersection theory has been introduced by S. Arakelov in order to provide a conceptual tool to measure the arithmetic complexity of rational points on algebraic varieties defined over number fields. Arakelov’s approach has been generalized by H. Gillet and C. Soulé to the higher dimensional setting. In this course we will provide a comprehensive introduction to arithmetic intersection theory and its latest developments.
We will start by reviewing classical intersection theory from algebraic geometry. Next we will give an introduction to the theory of Green’s currents, which can be seen as the differential geometric counterpart of algebraic geometric intersection theory. Combining these two theories will lead to arithmetic intersection theory, which will in particular provide the tool to measure the arithmetic complexity of closed subvarieties of algebraic varieties defined over number fields.
In the second part of the course we will talk about generalizations of the theory of arithmetic intersections, in particular to certain singular settings which enables us, among others, to apply the theory to Shimura varieties of non-compact type. In this context we will also discuss various examples.
The course will mainly be quite self-contained. As prerequisites we recommend a thorough knowledge of algebra and some basic knowledge in algebraic geometry and differential geometry. It is planned that we will design the exercise classes in the form of a student seminar which will be devoted to establish a thorough introduction to algebraic geometric intersection theory.
Ausgewählte Literatur
- William Fulton: Algebraic Curves, Addison-Wesley Publishing Company.
- William Fulton: Intersection Theory, Springer Verlag.
- Henri Gillet and Christophe Soulé: Arithmetic intersection theory, Publications mathématiques de l’I.H.É.S., tome 72 (1990), p. 93-174.
- Phillip Griffiths and Joseph Harris: Principles of Algebraic Geometry, John Wiley & Sons Inc.
- Robin Hartshorne: Algebraic Geometry, Springer Verlag.
- Christophe Soulé et al.: Lectures on Arakelov Geometry, Cambridge University Press.
Übung / Seminar
- Mittwoch, 11:15-12:45, online
- Beginn: Mittwoch, 22.04.2020, 11:15 Uhr
- Das Seminar findet online über die Plattform Zoom statt; die entsprechenden Links sind auf der entsprechenden Moodle-Homepage zu finden
- Für die Veranstaltung gibt es einen Moodle-Kurs. Sie müssen sich hier anmelden, um Kursmaterialien zu erhalten, an Diskussionen im Forum teilzunehmen und Mitteilungen von anderen Teilnehmern und Kursleitern zu erhalten. Wenn Sie kein CMS-Konto haben, können Sie ganz einfach ein externes Konto auf der Moodle-Homepage erstellen.
- Die Moodle-Homepage finden Sie hier: https://moodle.hu-berlin.de/course/view.php?id=93794
- Kursnummer: 3314424
- Kursname: Arithmetic Geometry (Vorlesung)
- Um den Einschreibeschlüssel für das Moodle zu erhalten, schicken Sie bitte eine E-Mail an Antareep Mandal.
Klausur
- Art: Digitale mündliche Prüfung
- Termin: 06.10.2020
- Anmeldung bis: 22.09.2020
- Rücktrittsfrist bis: 29.09.2020