M8195 Number theory seminar

Faculty of Science
Spring 2026
Extent and Intensity
0/2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: z (credit).
In-person direct teaching
Teacher(s)
Mgr. Pavel Francírek, Ph.D. (lecturer)
prof. RNDr. Radan Kučera, DSc. (lecturer)
Guaranteed by
prof. RNDr. Radan Kučera, DSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16. 2. to Fri 22. 5. Tue 14:00–15:50 M6,01011
Prerequisites
M3150 Algebra II
An understanding of the foundations of algebraic number theory, including local methods, p-adic analysis, and Galois theory of infinite extensions, is essential.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 6 fields of study the course is directly associated with, display
Abstract
This semester, we will build on the knowledge acquired in previous semesters. As in the previous semester, our main focus will be on the study of p-adic L-functions. However, this time we will not use the Kubota and Leopoldt method, but rather the Iwasawa method, which also provides certain connections between L-functions of different characters.
Learning outcomes
At the end of this course, students should be able to:
* define basic notions of the studied theory;
* explain learned theoretical results;
* apply learned methods to concrete exercises.
Key topics
Iwasawa's construction of p-adic L-functions.
Study resources and literature
  • WASHINGTON, Lawrence C. Introduction to cyclotomic fields. 2nd ed. New York: Springer, 1997, xiv, 487. ISBN 0387947620. info
Bookmarks
https://is.muni.cz/ln/tag/PříF:M8195!
Approaches, practices, and methods used in teaching
In this semester, we will meet in person. Home preparation will play an important role.
Method of verifying learning outcomes and course completion requirements
Credit will be given in case of active work in seminars - the study of the mentioned book during the term, regular solving of homework.
Language of instruction
Czech
Further Comments
The course is taught each semester.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Autumn 2010 - only for the accreditation, Spring 2005, Autumn 2005, Spring 2006, Autumn 2006, Spring 2007, Autumn 2007, Spring 2008, Autumn 2008, Spring 2009, Autumn 2009, Spring 2010, Autumn 2010, Spring 2011, Autumn 2011, Spring 2012, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Spring 2013, Autumn 2013, Spring 2014, Autumn 2014, Spring 2015, Autumn 2015, Spring 2016, Autumn 2016, Spring 2017, autumn 2017, spring 2018, Autumn 2018, Spring 2019, Autumn 2019, Spring 2020, Autumn 2020, Spring 2021, autumn 2021, Spring 2022, Autumn 2022, Spring 2023, Autumn 2023, Spring 2024, Autumn 2024, Spring 2025, Autumn 2025.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/spring2026/M8195