M Mueger
  • Member for 11 years, 2 months
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Tannaka duality for semisimple groups
9 votes

In order for ${\mathcal C}$ to come from an algebraic group rather than a pro-algebraic one, you want ${\mathcal C}$ to be finitely generated. And for semisimplicity, you want the group to have finite ...

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Prime Number Theorem w/o Complex Analysis
5 votes

A nice exposition of an Erdos/Selberg-type elementary proof is given by Levinson in Amer. Math. Monthly 76 (1969) 225–245. The proof by Daboussi as written up by Tenenbaum and Mendes-France was ...

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What is your favorite proof of Tychonoff's Theorem?
4 votes

I'm surprised that nobody has mentioned the proof using universal nets. (It can be found, e.g., in Pedersen's 'Analysis NOW' and in Bredon's 'Topology and geometry'.) A universal net in a set X is a ...

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Is Higher K-functor the derived functor of K0?
4 votes

The algebraic $K$-groups of a commutative unital ring can indeed be defined as derived functors, but one needs to work in the context of non-abelian homological algebra in the sense of A. Dold, D. ...

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What is your favorite proof of Tychonoff's Theorem?
3 votes

I have been teaching general topology for several years, but remained unsatisfied by the proofs given in the books that I based the course upon. Finally I wound up writing my own lecture notes, still ...

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Non-vanishing of zeta(s), Re(s)=1, without complex analysis?
3 votes

You might want to look at the paper "Le théorème des nombres premiers et la transformation de Fourier" by Jean-Benoît Bost, available at http://www.math.polytechnique.fr/xups/xups02-01.pdf It gives a ...

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English literature close to "Algébre et Théories Galoisiennes" by Régine and Adrien Douady
2 votes

An English translation of the book by the Douadys is scheduled to come out with Springer early in 2020.

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Applications of Brouwer's fixed point theorem
2 votes

The Perron-Frobenius theorem (in various degrees of generality) is an easy consequence of Brouwer's fixed-point theorem.

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