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Course10610446927 lectures

Computational Arithmetic - Geometry for Algebraic Curves

Prof. Nitin Saxena · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

week-01

  1. Lecture 01 Video
  2. Lecture 02 Video

week-02

  1. Lecture 03 : Dimension of Varieties Video
  2. Lecture 04 : Projective varieties Video

week-03

  1. Lecture 05 : Morphisms and rational functions Video
  2. Lecture 06 : Local rings Video

week-04

  1. Lecture 07 : Rational maps and Birationality Video
  2. Lecture 08 : Tangent space and Singularities Video

week-05

  1. Lecture 09 : Resolution of singularities Video
  2. Lecture 10 : Discrete valuation rings Video

week-06

  1. Lecture 11 : Existence of nonsingular model Video
  2. Lecture 12 : Nonsingular curves Video

week-07

  1. Lecture 13 : Divisor on Curves Video
  2. Lecture 14 : Riemann-Roch Spaces Video

week-08

  1. Lecture 15 : Riemann-Roch Spaces II Video
  2. Lecture 16 : Divisor Class Group Video

week-09

  1. Lecture 17 : Genus of a curve Video
  2. Lecture 18 : Riemann-Roch & Adeles Video

week-10

  1. Lecture 19 : Differentials and Riemann-Roch Video
  2. Lecture 20 : Canonical divisor and proof of Riemann-Roch Video

week-11

  1. Lecture 21 : Jacobian of a curve Video
  2. Lecture 22 : Zeta function of curves Video

week-12

  1. Lecture 23 : Functional equation & point counting Video
  2. Lecture 24 : Riemann hypothesis for curves Video
  3. Lecture 25 : Proof of RH for curves: Galois covers Video
  4. Lecture 26 : Proof of RH for curves II: Multilinear algebra Video
  5. Lecture 27 : Cohomological interpretation of zeta function Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Computer Science and Engineering
Teacher
Prof. Nitin Saxena
Level
Undergraduate
Language
English
Subjects
Computer science, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
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