# Computational Arithmetic - Geometry for Algebraic Curves

- Institution: IIT Kanpur
- Department: Computer Science and Engineering
- Teacher: Prof. Nitin Saxena
- Level: Undergraduate
- Language: English
- Subjects: Computer science, Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/106104469)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/106104469)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 01](https://invisiblenetwork.ai/learn/nptel/106104469/7037f400bbe9) (Video)
2. [Lecture 02](https://invisiblenetwork.ai/learn/nptel/106104469/c3539c0eee3a) (Video)
3. [Lecture 03 : Dimension of Varieties](https://invisiblenetwork.ai/learn/nptel/106104469/1c653b1f05db) (Video)
4. [Lecture 04 : Projective varieties](https://invisiblenetwork.ai/learn/nptel/106104469/f3ab647c9e3a) (Video)
5. [Lecture 05 : Morphisms and rational functions](https://invisiblenetwork.ai/learn/nptel/106104469/0c8dd03b7cc8) (Video)
6. [Lecture 06 : Local rings](https://invisiblenetwork.ai/learn/nptel/106104469/ee3d27dcaad3) (Video)
7. [Lecture 07 : Rational maps and Birationality](https://invisiblenetwork.ai/learn/nptel/106104469/efdf39da8744) (Video)
8. [Lecture 08 : Tangent space and Singularities](https://invisiblenetwork.ai/learn/nptel/106104469/d64ec3492e9c) (Video)
9. [Lecture 09 : Resolution of singularities](https://invisiblenetwork.ai/learn/nptel/106104469/99d2212fcae3) (Video)
10. [Lecture 10 : Discrete valuation rings](https://invisiblenetwork.ai/learn/nptel/106104469/30e4992978a2) (Video)
11. [Lecture 11 : Existence of nonsingular model](https://invisiblenetwork.ai/learn/nptel/106104469/9656c76b21e1) (Video)
12. [Lecture 12 : Nonsingular curves](https://invisiblenetwork.ai/learn/nptel/106104469/e531f14ff1cc) (Video)
13. [Lecture 13 : Divisor on Curves](https://invisiblenetwork.ai/learn/nptel/106104469/f35b9ff5fcd7) (Video)
14. [Lecture 14 : Riemann-Roch Spaces](https://invisiblenetwork.ai/learn/nptel/106104469/524e9c5aa7f7) (Video)
15. [Lecture 15 : Riemann-Roch Spaces II](https://invisiblenetwork.ai/learn/nptel/106104469/b7f8760afd4e) (Video)
16. [Lecture 16 : Divisor Class Group](https://invisiblenetwork.ai/learn/nptel/106104469/905381a8229c) (Video)
17. [Lecture 17 : Genus of a curve](https://invisiblenetwork.ai/learn/nptel/106104469/c50df9fb2f37) (Video)
18. [Lecture 18 : Riemann-Roch & Adeles](https://invisiblenetwork.ai/learn/nptel/106104469/fcbb7b6ceab4) (Video)
19. [Lecture 19 : Differentials and Riemann-Roch](https://invisiblenetwork.ai/learn/nptel/106104469/3a666e1f2a83) (Video)
20. [Lecture 20 : Canonical divisor and proof of Riemann-Roch](https://invisiblenetwork.ai/learn/nptel/106104469/5ca9f571eae8) (Video)
21. [Lecture 21 : Jacobian of a curve](https://invisiblenetwork.ai/learn/nptel/106104469/11fa487ab316) (Video)
22. [Lecture 22 : Zeta function of curves](https://invisiblenetwork.ai/learn/nptel/106104469/b6ca2a10cec0) (Video)
23. [Lecture 23 : Functional equation & point counting](https://invisiblenetwork.ai/learn/nptel/106104469/4e50c3aa652d) (Video)
24. [Lecture 24 : Riemann hypothesis for curves](https://invisiblenetwork.ai/learn/nptel/106104469/69b727b0d63c) (Video)
25. [Lecture 25 : Proof of RH for curves: Galois covers](https://invisiblenetwork.ai/learn/nptel/106104469/f39ae2b19987) (Video)
26. [Lecture 26 : Proof of RH for curves II: Multilinear algebra](https://invisiblenetwork.ai/learn/nptel/106104469/eea58c712772) (Video)
27. [Lecture 27 : Cohomological interpretation of zeta function](https://invisiblenetwork.ai/learn/nptel/106104469/d0694a8f944d) (Video)