# Mac Lane (co)homology of the second kind and Wieferich primes

@article{Efimov2015MacL,
title={Mac Lane (co)homology of the second kind and Wieferich primes},
author={Alexander I. Efimov},
journal={arXiv: Algebraic Geometry},
year={2015}
}
• A. Efimov
• Published 31 May 2015
• Mathematics
• arXiv: Algebraic Geometry
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…

## References

SHOWING 1-10 OF 37 REFERENCES
Homotopy finiteness of some DG categories from algebraic geometry
In this paper, we prove that the bounded derived category $D^b_{coh}(Y)$ of coherent sheaves on a separated scheme $Y$ of finite type over a field $\mathrm{k}$ of characteristic zero is homotopically
Cyclic homology of categories of matrix factorizations
In this paper, we will show that for a smooth quasi-projective variety over $\C,$ and a regular function $W:X\to \C,$ the periodic cyclic homology of the DG category of matrix factorizations
MODULI OF OBJECTS IN DG-CATEGORIES BY BERTRAND TOËN
– The purpose of this work is to prove the existence of an algebraic moduli classifying objects in a given triangulated category. To any dg-category T (over some base ring k), we define a D−-stack MT
Topological Hochschild homology of X(n)
We show that Ravenel's spectrum $X(2)$ is the versal $E_1$-$S$-algebra of characteristic $\eta$. This implies that every $E_1$-$S$-algebra $R$ of characteristic $\eta$ admits an $E_1$-ring map
The cyclotomic trace and algebraic K-theory of spaces
• Mathematics
• 1993
The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological refinement of cyclic homology. The target is naturally mapped to topological Hochschild homology, and
HOMOLOGY THEORIES FOR MULTIPLICATIVE SYSTEMS
• Mathematics
• 1951
with d[x]=0. It is convenient to augment ^4°(II) by regarding the commutator quotient group 11/ [II, II] as the group of O-dimensional chains, with d[x]=x[n, TI]. The complex ^4°(I1) occurs in a
Hochschild (co)homology of the second kind I
• Mathematics
• 2012
We define and study the Hochschild (co)homology of the second kind (known also as the Borel-Moore Hochschild homology and the compactly supported Hochschild cohomology) for curved DG-categories. An
Cohomology of algebraic theories
• Mathematics
• 1991
Cohomology theory for associative algebras over a field is due to Hochschild [9]. Generalization of this theory for associative algebras over a commutative ring K posed considerable complications.
WIEFERICH PAST AND FUTURE
Fermat’s Last Theorem (FLT) is the assertion that for n ≥ 3, the equation X + y = Z has no solutions in integers X,Y, Z with XY Z 6= 0. It was proven by Fermat for n = 4 and by Euler for n = 3, cf.
A hodge-type decomposition for commutative algebra cohomology
• Mathematics
• 1987
Abstract The Hochschild cohomology of a commutative algebra A of characteristic zero, with coefficients in a symmetric module M, decomposes into a direct sum Hn (A, M) = H1, n−1 + ∣ + Hn,0, where Hi,