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• Tags
  • #arithmetic-geometry/Langlands #open/problems
• Refs:
  • https://www.youtube.com/watch?v=vUFSgfeSa2A&list=PLCe-H2N8-ny7NtxoSNp8DTP3ic64MuY7G&index=8 #resources/videos
  • Course notes: rep theory of p-adic reductive groups https://www.math.columbia.edu/~phlee/CourseNotes/p-adicGroups.pdf#page=1 #resources/course-notes
  • Trace formula course notes: https://www.math.columbia.edu/~phlee/CourseNotes/TraceFormulae.pdf#page=1 #resources/course-notes
  • Notes: https://people.math.harvard.edu/~sli/papers/llc.pdf#page=1 #resources/notes
  • Notes for function fields: https://web.math.princeton.edu/~smorel/2014_Fall_MorelClass.pdf#page=2
• Links:
  • Geometric Langlands correspondence
  • Local Langlands correspondence
  • Global Langlands correspondence
  • arithmetic Langlands program
  • cyclotomic character
  • Tate twist
  • Congruence subgroup
  • algebraic group
  • locally symmetric space
  • Shimura variety
  • perverse sheaf
  • Unsorted/rigidity
  • Unsorted/tamely ramified
  • modular form

Langlands

L Functions

Topics

Pasted image 20211105233522.png Pasted image 20211106014758.png

• For deformation spaces of abelian varieties.
• https://www.wikiwand.com/en/Special_values_of_L-functions

Height pairing

Pasted image 20211106015333.png Pasted image 20211106015305.png

Examples

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Global Langlands