Related papers: On the 2-typical de Rham-Witt complex

The saturated de Rham-Witt complex, introduced by Bhatt-Lurie-Mathew, is a variant of the classical de Rham-Witt complex which provides a conceptual simplification of the construction and which is expected to produce better results for…

In an earlier paper, we defined and studied q-analogues of the Stirling numbers of both types for the Coxeter group of type B. In the present work, we show how this approach can be extended to all irreducible complex reflection groups G.…

We introduce a general constructive method to find a p-basis (and the Ulm invariants) of a finite Abelian p-group M. This algorithm is based on Groebner bases theory. We apply this method to determine the additive structure of…

It's well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall {\em explicitly} determine these structures related to multiple logarithms and some other multiple…

Using linear functional-based duality of modules, we generalize the syndrome decoding algorithm of linear codes over finite fields to those over finite commutative rings. Moreover, If the ring is local the algorithm is simplified by…

The set of periodic distributions, with usual addition and convolution, forms a ring, which is isomorphic, via taking a Fourier series expansion, to the ring ${\mathcal{S}}'({\mathbb{Z}}^d)$ of sequences of at most polynomial growth with…

We determine the structure over $\mathbb{Z}$ of the ring of symmetric Hermitian modular forms with respect to $\mathbb{Q}(\sqrt{-1})$ of degree $2$ (with a character), whose Fourier coefficients are integers. Namely, we give a set of…

In this paper, we fix a polynomial with complex coefficients and determine the eigenforms for SL2(Z) which can be expressed as the fixed polynomial evaluated at other eigenforms. In particular, we show that when one excludes trivial cases,…

In recent work with Bhatt and Morrow, we defined a new integral p-adic cohomology theory interpolating between etale and de Rham cohomology. An unexpected feature of this cohomology is that in coordinates, it can be computed by a…

We extend a classical fact about deformations of groups of units of commutative rings to $\mathbb{E}_{\infty}$-ring spectra, and we use this result to provide a map of spectra generalizing the ordinary logarithmic derivative induced by an…

In this brief essay a construction of the $2$-variable L-function of Langlands is sketched in terms of monomial resolutions of admissible representations of reductive locally $p$-adic Lie groups.

We determine simplicity criteria in characteristics 0 and $p$ for a ubiquitous class of iterated skew polynomial rings in two indeterminates over a base ring. One obstruction to simplicity is the possible existence of a canonical normal…

We show that a ring $\,R\,$ has two idempotents $\,e,e'\,$ with an invertible commutator $\,ee'-e'e\,$ if and only if $\,R \cong {\mathbb M}_2(S)\,$ for a ring $\,S\,$ in which $\,1\,$ is a sum of two units. In this case, the…

Two are the objectives of the present paper. First we study properties of a differentially simple commutative ring R with respect to a set D of derivations of R. Among the others we investigate the relation between the D-simplicity of R and…

The goal of this paper is to offer a new construction of the de Rham-Witt complex of smooth varieties over perfect fields of characteristic $p>0$. We introduce a category of cochain complexes equipped with an endomorphism $F$ of underlying…

This is the second in a sequence of three articles exploring the relationship between commutative algebras and $E_\infty$-algebras in characteristic $p$ and mixed characteristic. Given a topological space $X,$ we construct, in a manner…

We compute the moduli of endomorphisms of the de Rham and crystalline cohomology functors, viewed as a cohomology theory on smooth schemes over truncated Witt vectors. As applications of our result, we deduce Drinfeld's refinement of the…

Polynomial functions on the group of units Q_n of the ring Z_{2^n} are considered. A finite set of reduced polynomials RP_n in Z[x] that induces the polynomial functions on Q_n is determined. Each polynomial function on Q_n is induced by a…

Ritt's Second Theorem deals with composition collisions g o h = g* o h* of univariate polynomials over a field, where deg g = deg h*. Joseph Fels Ritt (1922) presented two types of such decompositions. His main result here is that these…

We study modular forms of some congruence subgroups. In this paper, we treat the cases level is 2-power, 3-power or 5. Structures of graded rings and many identities of infinite sum or infinite product are given. Theory of rational (1/3,…