# 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} }

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

- Mathematics
- 2013

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

- Mathematics
- 2012

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

- 2007

– 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)

- Mathematics
- 2017

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

- 2013

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,…