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Answers
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What is the insight of Quillen’s proof that all projective modules over a polynomial ring are free?
27
What is the knot associated to a prime?
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Non-commutative algebraic geometry
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What is the algebraic closure of the field with one element?
20
Applications of Noncommutative Geometry
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Rational numbers as an extension of the field with one element?
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Mazur’s unpublished manuscript on primes and knots?
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construct scheme from quivers?
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The work of E. Artin and F. K. Schmidt on (what are now called) the Weil conjectures.
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Representations of the three string braid group
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Dimension of subalgebras of a matrix algebra
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Non-smooth algebra with smooth representation variety
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Rationality of GIT quotients
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when are algebras quiver algebras ?
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Point modules of quantum projective space $\mathbb{P}^n$
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How to find examples of non-trival kernel of maps between Brauer groups Br(R) -> Br(K)
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Acyclic quivers differing only in arrow directions: functorial isomorphism of representation categories?
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Morita equivalence and moduli problems
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Existence of non-commutative desingularizations