Related papers: On some Rings of differentiable type

We give explicit descriptions of rings of differential operators of toric face rings in characteristic $0$. For quotients of normal affine semigroup rings by radical monomial ideals, we also identify which of their differential operators…

Let $(K,\nu)$ be an arbitrary-rank valued field, $R_\nu$ its valuation ring, $K(\alpha)/K$ a separable finite field extension generated over $K$ by a root of a monic irreducible polynomial $f\in R_\nu[X]$. We give necessary and sufficient…

Let $F$ be a field of characteristic $p$ and let $E/F$ be a purely inseparable field extension. We study the group $H_p^{n+1}(F)$ of classes of differential forms under the restriction map $H_p^{n+1}(F)\to H_p^{n+1}(E)$ and give a system of…

Let $(K, v)$ be a Henselian discrete valued field with a quasifinite residue field. This paper proves the existence of an algebraic extension $E/K$ satisfying the following: (i) $E$ has dimension dim$(E) \le 1$, i.e. the Brauer group Br$(E…

Let $R$ be a commutative ring of dimension $d$, $S = R[X]$ or $R[X, 1/X]$ and $P$ a finitely generated projective $S$ module of rank $r$. Then $P$ is cancellative if $P$ has a unimodular element and $r \geq d + 1$. Moreover if $r \geq \dim…

In characteristic zero, Zinovy Reichstein and the author generalized the usual relationship between irreducible Zariski closed subsets of the affine space, their defining ideals, coordinate rings, and function fields, to a non-commutative…

We show that any stack $\mathfrak{X}$ of finite type over a Noetherian scheme has a presentation $X \rightarrow \mathfrak{X}$ by a scheme of finite type such that $X(F) \rightarrow \mathfrak{X}(F)$ is onto, for every finite or real closed…

Let $R$ be a Henselian DVR with finite residue field. Let $G$ be a finite type, flat $R$-group scheme (not necessarily commutative) with smooth generic fiber. We show that $H^1_{\mathrm{fppf}}(\mathrm{Spec} R,G)$ is finite. We then give an…

Let $S$ be a submonoid of a free Abelian group of finite rank. We show that if $k$ is a field of prime characteristic such that the monoid $k$-algebra $k[S]$ is split $F$-regular, then $k[S]$ is a finitely generated $k$-algebra, or…

Let $(R,\mathfrak{m},K)$ be an $F$-finite Noetherian local ring which has a canonical ideal $I \subsetneq R$. We prove that if $R$ is $S_2$ and $H^{d-1}_{\mathfrak{m}}(R/I)$ is a simple $R\{F\}$-module, then $R$ is a strongly $F$-regular…

Let R be a semi-local regular domain containing an infinite perfect field k, and let K be the field of fractions of R. Let G be a reductive semi-simple simply connected R-group scheme such that each of its R-indecomposable factors is…

Let $R$ be a local ring of characteristic $p>0$ which is $F$-finite and has perfect residue field. We compute the generalized Hilbert-Kunz invariant for certain modules over several classes of rings: hypersurfaces of finite representation…

Let $K$ be a large field such that $K[\sqrt{-1}]$ is not algebraically closed and $F/K$ a function field in one variable. Extending techniques and results from earlier work with Becher and Dittmann, we show that every valuation ring on $F$…

We investigate the rings in which the set of nonzero elements is positive-existential (i.e. a finite union of projections of "algebraic" sets). In the case of Noetherian domains, we prove in particular that this condition is satisfied…

Let $D(s)$ be a fractional derivation of order $s$. For a real $p\ne 0$, we construct an integral operator $A(p)$ in an appropriate functional space such that $A(p) D(s) A(p)^{-1}=D(p s)$ for all $s$. The kernel of the operator $A(p)$ is…

Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. To any irreducible smooth…

Let F be a non-archimedean local field with residual characteristic p, and k an algebraically closed field of characteristic l different from p. We establish a category decomposition of Rep_k(SL_n(F) according to the GL_n(F)-inertially…

We prove that a complete local or graded one-dimensional domain of prime characteristic has finite F-representation type if its residue field is algebraically closed or finite, and present examples of a complete local or graded…

In this paper, we prove the following differential analog of the Noether normalization lemma: for every $d$-dimensional differential algebraic variety over differentially closed field of zero characteristic there exists a surjective map…

Let $S$ be a closed Riemann surface of genus $g \geq 2$ and $\varphi$ be a conformal automorphism of $S$, of prime order $p$ such that $S/\langle \varphi \rangle$ has genus zero. Let ${\mathbb K} \leq {\mathbb C}$ be a field of definition…