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- W580455258 abstract "In this paper we investigate the connection between the Mac Lane (co)homology and Wieferich primes in finite localizations of global number rings. Following the ideas of Polishchuk-Positselski cite{PP}, we define the Mac Lane (co)homology of the second kind of an associative ring with a central element. We compute this invariants for finite localizations of global number rings with an element $w$ and obtain that the result is closely related with the Wieferich primes to the base $w.$ In particular, for a given non-zero integer $w,$ the infiniteness of Wieferich primes to the base $w$ turns out to be equivalent to the following: for any positive integer $n,$ we have $HML^{II,0}(mathbb{Z}[frac1{n!}],w)nemathbb{Q}.$ As an application of our technique, we identify the ring structure on the Mac Lane cohomology of a global number ring and compute the Adams operations (introduced in this case by McCarthy cite{McC}) on its Mac Lane homology." @default.
- W580455258 created "2016-06-24" @default.
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- W580455258 date "2015-05-31" @default.
- W580455258 modified "2023-09-27" @default.
- W580455258 title "Mac Lane (co)homology of the second kind and Wieferich primes" @default.
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