Related papers: Witt-Burnside functor attached to $\mathbf{Z}_p^2$…

This is an introduction to the theory of Witt vectors. It includes a construction of the Witt rings, the Frobenius and Verschiebung endomorphisms, the canonical map from W to W^2 (its lambda-algebra structure), the relation to strict…

We combine Lurie's generalization of the Hopkins-Miller theorem with work of Zink-Lau on displays to give a functorial construction of even-periodic commutative ring spectra, concentrated in chromatic layers 2 and above, associated to…

We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat…

For an algebraic Hecke character defined on a CM field $F$ of degree $2d$, Katz constructed a $p$-adic $L$-function of $d+1+\delta_{F,p}$ variables in his innovative paper published in 1978, where $\delta_{F,p}$ denotes the Leopoldt defect…

Let G by compact p-adic Lie group and suppose that G is FAb, i.e., that H/[H,H] is finite for every open subgroup H of G. The representation zeta function Z(G,s) encodes the distribution of continuous irreducible complex characters of G.…

In arxiv:1602.04254, we have defined polynomial Witt vectors functor from vector spaces over a perfect field $k$ of positive characteristic $p$ to abelian groups. In this paper, we use polynomial Witt vectors to construct a functorial…

We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology $THH_{C_n}(-)$, and it describes the $E_2$ term of the K\"unneth spectral sequence for…

We give, for every finite group G, a combinatorial description of the ring of G-Witt vectors on a polynomial algebra over the integers. Using this description we show that the functor, which takes a ring with trivial action of G to its ring…

This paper is intended to provide foundations to the theory of Witt-type topological group and ring functors defined on a category of topological algebras, and, in presence of Banach norms, to show how to topologically deal with them. It is…

Let k be an arbitrary field (of arbitrary characteristic) and let X = [x_{i,j}] be a generic m x n matrix of variables. Denote by I_2(X) the ideal in k[X] = k[x_{i,j}: i = 1, ..., m; j = 1, ..., n] generated by the 2 x 2 minors of X. We…

We prove that the KZ functor from a certain category of modules for the Cherednik algebra to finite dimensional modules over the Hecke algebra is essentially surjective. Then we begin to use this result to study the analog of category O for…

Let E be a Dedekind complete Riesz space with weak unit e, equipped with a conditional expectation operator T. We prove that the spaces Lp(T), with their natural vector-valued norms, are strongly complete, extending the p=2 case of Kuo,…

We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As…

Let $p \neq 2$. For any small enough $r> \max \{p-1,1\}$ and for any $\Lambda > 1$ there exists a Lipschitz function $u$ and a bounded vectorfield $f$ such that \[ \begin{cases} {\rm div}(|\nabla u|^{p-2} \nabla u) = {\rm div} (f) \quad&…

We provide a Rademacher theorem for intrinsically Lipschitz functions $\phi:U\subseteq \mathbb W\to \mathbb L$, where $U$ is a Borel set, $\mathbb W$ and $\mathbb L$ are complementary subgroups of a Carnot group, where we require that…

We study the algebraic $K$-theory of the ring of continuous functions on a compact Hausdorff space with values in a local division ring, e.g., a local field: We compute its negative $K$-theory and show its $K$-regularity. The complex case…

We study representation zeta functions of finitely generated, torsion-free nilpotent groups which are rational points of unipotent group schemes over rings of integers of number fields. Using the Kirillov orbit method and p-adic…

The rings of $p$-typical Witt vectors are interpreted as spaces of vanishing cycles for some perverse sheaves over a disc. This allows to "localize"\ an isomorphism emerging in Drinfeld's theory of prismatization [Dr], Prop. 3.5.1, namely…

In this work we study $p$-adic continuous functions in several variables taking values on $\mathbb{Z}_p$. We describe the orthonormal van der Put base of these functions and study various Lipschitz conditions in several variables,…

The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A_inf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline…