TU Kaiserslautern • Department of Mathematics • Summer 2016

Seminar «Topics in Algebra and Geometry»

Prof. Dr. Mathias Schulze • Dipl.-Math. Dipl.-Phys. Philipp Korell

Meetings

The seminar takes place Tuesdays from 1:45pm to 3:15pm in room 48-438. In the first week of the semester we will have an organizational meeting. The first talk will be given on May 17 (or possibly on April 26).

Topics

The seminar will cover independend topics of general interest. As the anticipated group of participants and audience will be quite diverse the material needs to be presented in a self contained and generally understandable way. The focus will lie on explaining ideas and concepts instead of covering and proving all technical details.

Topics for talks will be assigned on an individual basis based on your personal background and interest. You may suggest a topic yourself, or I can make suggestions. If you consider attending the seminar, or if you just need some more information, please contact me by email asap.

Talks

Meeting	Date(s)	Speaker	Title
0	19.04.2016	Mathias Schulze	Organizational Meeting
1	26.04.2016	Christoph Lampe	Category Theory
2a 2b	17.05.2016	Christoph Lampe Bastian Heinen	Morita Equivalence Projective and Injective Modules
3	24.05.2016	Eva Maria Hemmerling	Completion
4	31.05.2016	Kerstin Klein	Valuations and Valuation Rings
5	7.06.2016	Daniel Berhanu	Extensions and Ext functors
6	14.06.2016	Ali Aslam	Grade, Depth and Cohen-Macaulay
7	28.06.2016	Bastian Heinen	Derivations
8	5.07.2016	Bastian Heinen	Separable Extensions
9	12.07.2016	George Krait	Zariski's Main Theorem

Credit Points

Anyone is welcome to attend the seminar talks. To gain credit points you need to give a good talk.

Literature

1 Category Theory

Adamek-Herrlich-Strecker, Abstract and Concrete Categories, Ch. 1
Mac Lane, Categories for the Working Mathematician, Ch. 1
The nLab

2a Morita Equivalence

Cohn, Further Algebra and applications, Ch. 4.4

2b Projective and Injective Modules

3 Completion

Eisenbud, Commutative Algebra with a View towards Algebraic Geometry, Ch. 7
Altman-Kleiman, Introduction to Grothendieck duality, II.1

4 Valuations and Valuation Rings

Ash, A Course In Commutative Algebra, Ch. 3
Lorenz, Einführung in die Algebra II, Ch. 23

5 Extensions and Ext functors

Hilton-Stammbach, A Course in Homological Algebra, III.1-2, IV.9
Collins, Homological Algebra, §6
May, Notes on Tor and Ext, §4

6 Grade, Depth and Cohen-Macaulay

Ash, A Course In Commutative Algebra, Ch. 6
Eisenbud, Commutative Algebra with a View towards Algebraic Geometry, Ch. 18
Bruns-Herzog, Cohen-Macaulay Rings, I.1.2,2.1

7 Derivations

8 Separable Extensions

9 Zariski's Main Theorem

Liu, Algebraic Geometry, 4.4
Hartshorne, Algebraic Geometry, III.11
Swant, Zariski’s Main Theorem
Chiu, Zariski's Main Theorem, Masterarbeit

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