Algebraic Geometry Cross World

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Across
  1. 3. setting for linear algebra over rings
  2. 7. died in a duel
  3. 9. hard boundary
  4. 11. mirrors structure
  5. 14. a computational tool
  6. 15. reduced by a prime
  7. 17. transforming between functors
  8. 19. (m_x/m_x^2)
  9. 23. divide those polynomials
  10. 24. 1-dimensional spaces
  11. 26. intersect those things sortof
  12. 27. degree two
  13. 29. a big bag of number-like things
  14. 30. land of the homogeneous
  15. 34. structures with transformations
  16. 35. makes modules sexy but stupid
  17. 37. algebraic notion of functions
  18. 40. soft boundary
  19. 45. extrapolating the idea of a sum
  20. 47. fundamental theorem about zeros
  21. 48. can always be nicely covered
  22. 49. boring 1-dimensional spaces
  23. 50. lots of glue
  24. 52. extrapolating the idea of a product
  25. 53. study of stretchy stuff
  26. 56. when homology is trivial
  27. 59. preserves structure
  28. 61. a formal symbol
  29. 62. the geometric analogue of a ring
  30. 64. differentials square to nothing
  31. 66. everything that can be touched
  32. 67. the image is the kernel
  33. 70. triangles and their upgrades
  34. 72. no secret zeros
  35. 73. every point knows every other point
  36. 75. looking at a point
  37. 77. (m_x/m_x^2)^\ast
  38. 78. only need one generator
Down
  1. 1. nothing lasts forever
  2. 2. gotta count the poles
  3. 4. might have enough glue
  4. 5. better infinitely longer polynomials
  5. 6. a big bag of symmetries
  6. 8. polynomials minus the addition
  7. 9. degree three
  8. 10. cancel from the left
  9. 12. zooming into a sheaf
  10. 13. makes linear into multilinear
  11. 16. no relations
  12. 18. something derived from the left
  13. 20. topologised this shit
  14. 21. cancels from the right
  15. 22. 2-dimensional spaces
  16. 25. defined by polynomial equations
  17. 28. line bundles with nonnegative degree on every curve in the variety
  18. 31. a bag full of all primes
  19. 32. walking around in loops
  20. 33. genus one
  21. 35. distributes over composition
  22. 36. useful sequences for computing homology
  23. 38. nilpotents on the cheap
  24. 39. an important parameter space
  25. 41. Jacobian matrix has big rank
  26. 42. ab in p implies a in p or b in p
  27. 43. can be unmultiplied from things
  28. 44. display those relations
  29. 46. no one knows why this word is used for this anymore
  30. 51. homomorphism from a ring
  31. 54. separated of finite type and universally closed
  32. 55. the next step after a sheaf
  33. 57. travel must reverse direction
  34. 58. can quotient a group when ...
  35. 60. made out of line bundles
  36. 63. can scramble multiplications without issue
  37. 65. linear algebra for the fanciful
  38. 68. restrictions are surjective
  39. 69. the study of rings
  40. 71. spec for a graded ring
  41. 74. something derived from the right
  42. 76. everything sent to zero