Let S be an unramified regular local ring of mixed characteristic p≥3 and Sp the subring obtained by lifting to image Frobenius map on S/pS. R integral closure in a biradical extension degree p2 its quotient field adjoining p-th roots sufficiently general square free elements f,g∈Sp. We show that admits birational maximal Cohen-Macaulay module. It is noted not automatically Cohen-Macaulay.

We construct an action of the Neron–Severi part Looijenga–Lunts–Verbitsky Lie algebra on Chow ring Hilbert scheme points a K3 surface. This yields simplification Maulik and Negut’s proof that cycle class map is injective subring generated by divisor classes as conjectured Beauville. The key step in construction explicit formula for Lefschetz duals terms Nakajima operators. Our results also lead...

For n = 2 − 4, m > 2, we determine the cup-length of H∗(G̃n,3;Z/2) by finding a Gröbner basis associated with a certain subring, where G̃n,3 is the oriented Grassmann manifold SO(n + 3)/SO(n)× SO(3). As an application, we provide not only a lower but also an upper bound for the LS-category of G̃n,3. We also study the immersion problem of G̃n,3.

Given two rings R ⊆ S, S is said to be a minimal ring extension of R if R is a maximal subring of S. In this article, we study minimal extensions of an arbitrary ring R, with particular focus on those possessing nonzero ideals that intersect R trivially. We will also classify the minimal ring extensions of prime rings, generalizing results of Dobbs, Dobbs & Shapiro, and Ferrand & Olivier on com...

Let F be a field, let D be a subring of F , and let X be the Zariski-Riemann space of valuation rings containing D and having quotient field F . We consider the Zariski, inverse and patch topologies on X when viewed as a projective limit of projective integral schemes having function field contained in F , and we characterize the locally ringed subspaces of X that are affine schemes.

The moduli space of curves has proven itself a central object in geometry. The past decade has seen substantial progress in understanding the moduli space of curves, involving ideas, for example, from geometry (algebraic, symplectic, and differential), physics, topology, and combinatorics. Many of the new ideas are related to the tautological ring of the moduli space, a subring of the cohomolog...

We characterize ring spectra morphisms from the algebraic cobordism spectrum MGL ([12]) to an oriented spectrum E (in the sense of Morel [4]) via formal group laws on the ”topological” subring E∗ = ⊕iE 2i,i of E∗∗. This result is then used to construct for any prime p a motivic Quillen idempotent on MGL(p). This defines the BP -spectrum associated to the prime p as in Quillen’s [6] for the comp...

If R is an integral domain and K is its field of fractions, we let Int(R) stand for the subring of K[x] which maps R into itself. We show that if R is the ring of integers of a p-adic field, then Int(R) is generated, as an R-algebra, by the coefficients of the endomorphisms of any Lubin-Tate group attached to R.

In answering questions from [7] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V , and let st : V → k be the corresponding standard part map. Under a mild assumption on (R, V) we show that definable sets X ⊆ V n admit a triangulation that induces a triangulation of its standard part st(X) ⊆ k n .

In this paper, we introduce the Harish-Chandra homomorphism for quantum superalgebra $$\mathrm {U}_q({\mathfrak {g}})$$ associated with a simple basic Lie $${\mathfrak {g}}$$ and give an explicit description of its image. We use it to prove that center is isomorphic subring ring $$J({\mathfrak exponential super-invariants in sense Sergeev Veselov, establishing type theorem . As byproduct, obtai...