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Next lecture is on Thursday 29/11. I will then talk about abelian varieties, with a view towards how the theory and results we have proved for elliptic curves generalize to higher dimension.
Note that there is no lecture on Tuesday 27/11.
I have now uploaded a syllabus for MAT4230, containing information on what is concidered the syllabus for the course. In particular, you will find explicitly which parts of the book we did not cover (and hence you will not be asked about it on the exam).
I have now uploaded the pdf-file "Exam-info", which contains useful information regarding the oral exam on Dec. 6. Please read through it, and feel free to ask me any time if you have any questions.
I have now uploaded a new set of exercises; "Exercises 6".
Next lecture is on Tuesday 13/11, time and place as usual. I will introduce zeta functions, and formulate the Weil conjectures. Then I will start to discuss the proof of the Weil conjectures for elliptic curves. This will be continued, and probably finished in the lecture on Thursday 15/11.
Oral exam: The oral exam will be held on December 6th. All students who are signed up for the subject should have received an e-mail about the exam. If not - please send an e-mail to: studieinfo@math.uio.no
On Thursday and Friday this week our group is hosting the "National Algebra Meeting", with many talks on a variety of topics in Algebra and Algebraic Geometry. Check the website of the math department for further info.
Next lecture is on Tuesday 06/11, time and place as usual. I will close off the discussion on the Weil pairing, and then we have covered all of Chapter III in the book!
In the lecture on thursday, I will first explain some of the exercises from exercise sheets 4&5. In the remaining time, I will start discussing Chapter V, Section 1.
Next lecture is on Tuesday 30/10, time and place as usual. I will then finish the discussion on Endomorphism algebras of Elliptic curve (Section III.9) and I will also talk about (the very short) Section III.10, concerning the automorphism group.
On Thursday 1/11, I will start talking about Section III.8, concerning the Weil pairing, which is quite important when we later consider elliptic curves over finite fields.
I have now put up a new set of exercises, "Exercises 5", on the webpage. Some of the exercises are things I conveniently "left as exercises" during the lectures. If you are busy working on the assignment, it is no problem postponing looking at these new problems for a week or two, but it may be useful to have seen and thought about these things before we start talking about Chapter V in a few weeks time.
Next lecture is on Tuesday 23/10, time and place as usual. I will continue the discussion on dual isogenies. In the lecture on Thursday 25/10, I will finish Section 6 on dual isogenies, and move on to Chapter III, Section 7 (The Tate module).
Next lecture is on Tuesday 16/10, time and place as usual. I will continue to talk about the Frobenius morphism. In the lecture on Thursday 18/10, I will first finish the discussion of Section 5 in Chapter III, and I will start with Section 6, which is about the "dual" isogeny.
I have now modified the exercises in the 4th set of exercises. The new version is available if you clock the link "Exercises 4" on this homepage.
After the lecture on Tuesday 09/10, I will hand out the mandatory assignment. (I will also put up a pdf-file on the homepage.)
Please hand in your solutions (to me) by Tuesday 30 of October. If you have any questions, you are very welcome to send me an email or drop by my office.
Good luck!
Next lecture is on Tuesday 09/10, time and place as usual. I will then go through some of the exercises from sheets 3&4.
In the lecture on Thursday 11/10, I will start discussing the material in Chapter III, Section 5 (about the invariant differential).
Next lecture is on Tuesday 02/10, time and place as usual. I will start lecturing from Chapter III, Section 4 (about isogenies). This will be continued in the lecture on Thursday 04/10.
You'll find a new set of exercises (Exercises 4) on this homepage. They concern what we've discussed so far in Chapter III.
There will be one written assignment during the semester. If you plan to take the exam in this course, this assignment must be passed first. I will come back to this in the lectures, and keep you informed on this homepage. The plan is to hand out the assignment in the second week of October, the deadline will be appr. 3 weeks after that.
Next lecture is on Tuesday 25/9, time and place as usual. I will start lecturing from Chapter III, Section 3 in the book. This will be continued in the lecture on Thursday 27/9.
You'll find a new set of exercises (Exercises 3) on this webpage. They are based on the material in the first two sections of Chapter III in the book.
Next lecture is tomorrow, tuesday 18/09 at 12:15 in room B62. I will talk about the remaining part in Section 1 of Chapter III in Silverman's book.
On thursday I will discuss the material in Section 2 of Chapter III.
I'm away next week, this means that we will postpone the lecture on Tuesday 11.09. We'll find a suitable time later in the semester.
On Thursday 13.09, the lecture will go ahead as usual, with a discussion of (some of) the exercises from Exercise sheets 1&2.
In todays lecture, we started discussing Chapter III in Silverman, in particular proving Proposition 1.4.
In todays lecture we more or less covered material from II.2-4 in Silverman's book, ending with the introduction of differentials and defining divisors from differentials on a smooth curve.
Next lecture is on Tuesday 04.09, 12:15-13:00 as usual. Then II.5 will be discussed, where we get further acquainted with divisors on curves. In particular, we study the Riemann-Roch formula, and define the genus of an algebraic curve.
After this, we have all the tools we need to start talking about elliptic curves. This will be the topic of the lecture on Thursday 06.09. I will then start lecturing from Chapter III in Silveman's book.
Next lecture is tuesday 28.08 at 12:15-13:00, room B62 in NHA. I will start discussing the material in Chapter 2 in Silverman's book.