Related papers: Valuation rings are derived splinters
Differential algebraic geometry seeks to extend the results of its algebraic counterpart to objects defined by differential equations. Many notions, such as that of a projective algebraic variety, have close differential analogues but their…
This is the fourth part in the series of articles math.MG/0503397, math.MG/0503399, math.MG/0509512 where the theory of valuations on manifolds is developed. In this part it is shown that the filtration on valuations introduced in…
A complete classification of unimodular valuations on the set of lattice polygons with values in the spaces of polynomials and formal power series, respectively, is established. The valuations are classified in terms of their behaviour with…
In this paper, we introduce a new class of derivations that generalizes skew derivations and semi-derivations, and we call it ``skew semi-derivation". Further, we present a study of the conditions under which this type of multiplicative…
We prove the weight part of Serre's conjecture in generic situations for forms of $U(3)$ which are compact at infinity and split at places dividing $p$ as conjectured by Herzig. We also prove automorphy lifting theorems in dimension three.…
The main purpose of this paper is to study and investigate concerning a ({\alpha},{\alpha})-symmetric derivations D on semiprime rings and prime rings R, we give some results when R admits a ({\alpha},{\alpha})-symmetric derivations D to…
This work is concerned with categorical methods for studying singularities. Our focus is on birational derived splinters, which is a notion that extends the definition of rational singularities beyond varieties over fields of characteristic…
In this paper we provide necessary and sufficient conditions for $ R=A\propto E $ to be a valuation ring where $E$ is a non-torsion or finitely generated $A-$module. Also, we investigate the $ (n,d) $ property of the valuation ring.
We investigate ideal-semisimple and congruence-semisimple semirings. We give several new characterizations of such semirings using e-projective and e-injective semimodules. We extend several characterizations of semisimple rings to (not…
A ring is *unit-additive* if a sum of units is always either a unit or nilpotent. For example, $k[X]$ and $k[X]/(X^2)$ are unit-additive, but $\mathbb Z$ is not. We prove a wide-ranging theorem about unit-additivity in semigroup rings,…
We establish various properties of the p-adic algebraic K-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the p-adic K-theory of such rings is homotopy invariant, and coincides with the…
A Noetherian reduced ring $A$ is called a birational derived splinter if for all proper birational maps $X\to\operatorname{Spec}(A)$, the canonical map $A\to Rf_*\mathcal{O}_X$ splits. In equal characteristic zero this property…
We prove $p$-complete arc-descent results for finite projective modules and perfect complexes over integral perfectoid rings. Using our results, we clarify a reduction argument in the proof of the classification of $p$-divisible groups over…
We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…
We consider skew free extensions of rings, also known as free multivariate skew polynomial rings, and explore some of the algebraic aspects of this construction. We give different characterizations of such rings and present conditions for…
Let $A$ and $B$ be two connected graded algebras finitely generated in degree one. If $A$ is isomorphic to $B$ as ungraded algebras, then they are also isomorphic to each other as graded algebras.
L. Szpiro and T. Tucker recently proved that under mild conditions, the valuation of the minimal discriminant of an elliptic curve with semistable reduction over a discrete valuation ring can be expressed in terms of intersections between…
A ring R is said to be VNL if for any a in R, either a or 1-a is (von Neumann) regular. The class of VNL rings lies properly between the exchange rings and (von Neumann) regular rings. We characterize abelian VNL rings. We also characterize…
We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…
Let $(K,v)$ be a valued field. We review some results of MacLane and Vaqui\'e on extensions of $v$ to valuations on the polynomial ring $K[x]$. We introduce certain MacLane-Vaqui\'e chains of residually transcendental valuations, and we…