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6 votes
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How to extend Ritt's theorem on elementary invertible bijective elementary functions?

The elementary functions according to Liouville and Ritt are the functions of a complex variable built up by applying exponentiation, logarithms and/or algebraic operations finitely often. That means, ...
IV_'s user avatar
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4 votes
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356 views

Jet Nestruev's proof that the exterior derivative $d$ on a real line is not a Kähler differential $d_{C^\infty(\mathbb{R})/\mathbb{R}}$

The relation between the exterior derivative $d:C^\infty(\mathbb{R})\to\Omega^1\mathbb(\mathbb{R})$ and the Kähler differential $d_{C^\infty(\mathbb{R})/\mathbb{R}}:C^\infty(\mathbb{R})\to\Omega_{C^\...
Fallen Apart's user avatar
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2 votes
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213 views

Open problems in differential algebra and affine algebraic geometry

I am currently doing a PhD in differential algebra and affine algebraic geometry at the University of Buenos Aires. I've been struggling to find a list of interesting and big open problems in these ...