2019 Special courses on advanced topics in Mathematics G

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Academic unit or major
Mathematics
Instructor(s)
Abe Noriyuki 
Course component(s)
Lecture
Day/Period(Room No.)
Intensive ()  
Group
-
Course number
ZUA.E341
Credits
2
Academic year
2019
Offered quarter
1Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

The mod p representation (representations defined over characteristic p field) theory is getting important mainly because of mod p Langlands correspondence. In this lecture, I will talk about mod p representaiton theoy and representation theory of pro-p-Iwahori Hecke algebra.

Student learning outcomes

Understanding the classification theorem of irreducible admissible mod p representations. Can do calculations related to pro-p-Iwahori Hecke algebra.

Keywords

p-adic reductive group, mod p renresentations, irreducible representations.

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- - - -

Class flow

This is a standard lecture course.

Course schedule/Required learning

  Course schedule Required learning
Class 1 (1) Hecke algebra (2) The structure of pro-p-Iwahori Hecke algebra (3) Representation theory of pro-p-Iwahori Hecke algebra (4) Relations with mod p representations (5) Classification of irreducible admissible mod p renresentations. Details will be provided during each class session

Textbook(s)

None required

Reference books, course materials, etc.

none

Assessment criteria and methods

Assignments (100%).

Related courses

  • MTH.A301 : Algebra I
  • MTH.A302 : Algebra II
  • MTH.A331 : Algebra III

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None required

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