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I think there are many reasons. Here are a few. Practical reasons Cohen-Macaulay rings are just plain easier to work with. Computations in local cohomology For example, any number of computatio …

In the case of a single variable, see for example this article concerning the limit $\lim_{n\to\infty}f^{(n)}(x)$ for a smooth function $f:\mathbb R\to\mathbb R$. Also, if $f:\mathbb R\to\mathbb R$ i …

Let $\alpha \in \pi_s(S^0)$ for $s > 0$ be an element of positive degree in the stable stems. Then $\alpha$ has positive-dimensional filtration in the Adams-Novikov spectral sequence: in other words, …

The answer to your question is yes, of course. The theory has been around at least since the late 60s! See Wasserman's paper A Wasserman. Equivariant differential topology, Topology 1969; 8(2):12 …

You cannot obtain an example from odometers because they have discrete point spectrum. It is not true in the topological setting- look at example 7.4.19 from http://books.google.ca/books/about/An_In …

The relation is $\zeta(4,1)=2\zeta(5)-\zeta(2)\zeta(3)$. It can be found, for example, in http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.pjm/1102636166&page=record (M …

A proof for the class $\mathcal{C}$ group-subgroup subfactors: First of all, by the Galois correspondence, an intermediate subfactor $R^G \subset P \subset R^H$ is given by an intermediate subg …

This is an artificial answer, I'm looking for something more natural. In this paper, T. Teruya introduced the notion of normal intermediate subfactors, generalizing exactly the notion of normal sub …

For the generalization in the first direction, the $p$-rank of the incidence matrix $N$ of an $S(2,k,v)$ is lower bounded by the dimension of the Steinberg module: $$\operatorname{rank}_2(N)(\operato …

The dynamics are ergodic with respect to Lebesgue measure. See G. Hedlund, Fuchsian groups and mixtures, Ann. of Math. Volume 40, Number 2 (1939) 370-383, available here. If you prefer somethi …

If you are really satisfied with a model only of the theory $Q$, then you should be prepared for a bad situation, for this is an extremely weak theory. In fact one can make a computable model simply b …

The spectrum of the Dirac operator on spheres was computed by Christian Bär: http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.jmsj/1226499694&page=record See also th …

I think the correct reference should be Theorem 1 in Tadashi NAGANO, Linear differential systems with singularities and an application to transitive Lie algebras, J. Math. Soc. Japan Volume 18, Numbe …

In Pacific Journal of Math 4 (1954), pp 219-226, Marshall Hall, Jr. writes in the paper "On a theorem of Jordan" that: In 1872, Jordan showed that a finite quadruply transitive group in which only …