Learn · Computational Arithmetic - Geometry for Algebraic Curves

Lecture 19 of 27week-10

Lecture 19 : Differentials and Riemann-Roch

Prof. Nitin Saxena · IIT Kanpur

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Computational Arithmetic - Geometry for Algebraic Curves, IIT Kanpur (at NPTEL)
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All the lectures

  1. Lecture 01 Video
  2. Lecture 02 Video
  3. Lecture 03 : Dimension of Varieties Video
  4. Lecture 04 : Projective varieties Video
  5. Lecture 05 : Morphisms and rational functions Video
  6. Lecture 06 : Local rings Video
  7. Lecture 07 : Rational maps and Birationality Video
  8. Lecture 08 : Tangent space and Singularities Video
  9. Lecture 09 : Resolution of singularities Video
  10. Lecture 10 : Discrete valuation rings Video
  11. Lecture 11 : Existence of nonsingular model Video
  12. Lecture 12 : Nonsingular curves Video
  13. Lecture 13 : Divisor on Curves Video
  14. Lecture 14 : Riemann-Roch Spaces Video
  15. Lecture 15 : Riemann-Roch Spaces II Video
  16. Lecture 16 : Divisor Class Group Video
  17. Lecture 17 : Genus of a curve Video
  18. Lecture 18 : Riemann-Roch & Adeles Video
  19. Lecture 19 : Differentials and Riemann-Roch Video
  20. Lecture 20 : Canonical divisor and proof of Riemann-Roch Video
  21. Lecture 21 : Jacobian of a curve Video
  22. Lecture 22 : Zeta function of curves Video
  23. Lecture 23 : Functional equation & point counting Video
  24. Lecture 24 : Riemann hypothesis for curves Video
  25. Lecture 25 : Proof of RH for curves: Galois covers Video
  26. Lecture 26 : Proof of RH for curves II: Multilinear algebra Video
  27. Lecture 27 : Cohomological interpretation of zeta function Video