On a comparison theorem

On the Cohomology Comparison Theorem

A relative derived category for the category of modules over a presheaf of algebras is constructed to identify the relative Yoneda and Hochschild cohomologies with its homomorphism groups. The properties of a functor between this category and the relative derived category of modules over the algebra associated to the presheaf are studied. We obtain a generalization of the Special Cohomology Com...

A note on spectral mapping theorem

This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

On Izumi’s Theorem on Comparison of Valuations

We prove that the sequence of MacLane key polynomials constructed in [7] and [3] for a valuation extension (K, ν) ⊂ (K(x), μ) is finite, provided that both ν and μ are divisorial and μ is centered over an analytically irreducible local domain (R,m) ⊂ K[x]. As a corollary, we prove Izumi’s theorem on comparison of divisorial valuations. We give explicit bounds for the Izumi constant in terms of ...

Some Results on Baer's Theorem

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

An isoperimetric comparison theorem