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Fearless Symmetry by Robert Gross, Avner Ash

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270 INDEX
Ellenberg, Jordan, 259
elliptic curve, 103–113, 146–147,
205–215, 230, 231, 239–240
conductor, 246
modular, 251
torsion, 111–113, 146, 209–215
equations
coupled, 56
uncoupled, 56
´
etale cohomology, 225, 229–232, 236,
260
Euler, Leonhard, 122
! (factorial), 8
F
p
,36
Fermat’s Last Theorem, 55, 109, 242–
256
Fermat, Pierre de, 52
field, 36, 150
finite flat group scheme, 236
fixed field, 189
Fontaine, Jean-Marc, 231
Fontaine–Mazur Conjecture, 231
Four Color Theorem, 65
Fourier coefficients, 236
Frey curves, 245
Frey, Gerhard, 245
Frobenius, 177–190
Frobenius, Georg, 177
Frob
(complex conjugation), 178
Frob
p
, 178
function, 7, 23
G( f ), 150–158, 160, 175, 238
GL(n, R), 129
G
Q
. See absolute Galois group of Q
Galois group. See group, Galois
Galois representation. See represen-
tation, Galois
Galois theory, 87–102
Gauss, Carl Friedrich, xviii, xxvii, 31,
33, 48
G
¨
odel, Kurt, 235
Graeco-Latin Square, 122, 123
greatest common divisor, 6
Grothendieck, Alexander, 232
group, 1–30
abelian, 103
cohomology, 229
commutative, 40
continuous, 5
cyclic, 40
definition, 4
discrete, 5
formal, 236
Galois, 61, 66, 149–156
generator, 40
isomorphic, 154
law, 4
closed, 125
Lie, 5
linear, 115
matrix, 124–134
monodromy, 229
permutation, 21–30
ι, 152
I (identity matrix), 126
ideal, 189
prime, 190
identity permutation, 25
integer, 34
inverse Galois problem, 154–155
invertible transformation, 60
k
n
, 226
kernel, 188
Lang, Serge, 103
Langlands, Robert, 240, 254
Legendre symbol, 71, 219
multiplicativity, 73
Leibniz, Gottfried, 52, 73
lemma, 47
Lie, Sophus, 5
linear action, 227

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