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Fundamental group of the moduli stack of elliptic curves

What is the possible usefulness of étale topology and cohomology apart from the resolution of the Weil conjecture ?

Arithmetic geometry examples

Punctured spectrums of local rings

Why $\partial$ and $\bar{\partial}$ defined in that way (the Wirtinger derivatives)?

homomorphism into reductive groups

homogeneous polynomials over a finite field

orthogonal group over local field

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ag.algebraic-geometry× 5
nt.number-theory× 2
finite-fields
examples
elliptic-curves
cv.complex-variables
complex-analysis
big-list
arithmetic-geometry
algebraic-groups

ac.commutative-algebra
4-manifold
3-manifolds

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