Related papers: GAGA for Henselian schemes

The global analogue of a Henselian local ring is a Henselian pair: a ring A and an ideal I which satisfy a condition resembling Hensel's lemma regarding lifting coprime factorizations of polynomials over A/I to factorizations over A. The…

Let $R$ be the henselization of a local ring of a semistable family over the spectrum of a discrete valuation ring of mixed characteristic $(0, p)$ and $k$ the residue field of $R$. In this paper, we prove an isomorphism of \'{e}tale…

We show the Gersten's conjecture for \'etale cohomology over two dimensional henselian regular local rings without assuming equi-characteristic. As application, we obtain the local-global principle for Galois cohomology over mixed…

The main result of the paper states that for a graded ideal I in a polynomial ring R over a field of characteristic 0, the Hilbert functions of the local cohomology modules of R/I and of R/Gin(I) coincide if and only if R/I is sequentially…

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of…

In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…

We study a Grothendieck topology on schemes which we call the $\mathrm{arc}$-topology. This topology is a refinement of the $v$-topology (the pro-version of Voevodsky's $h$-topology) where covers are tested via rank $\leq 1$ valuation…

A semiring scheme generalizes a scheme in such a way that the underlying algebra is that of semirings. We generalize \v{C}ech cohomology theory and invertible sheaves to semiring schemes. In particular, when $X=\mathbb{P}^n_M$, a projective…

We compute the completion of the local ring of the Hilbert scheme of degree $n+1$ subschemes of $\mathbb{A}^n$ at the point corresponding to the ideal $\langle x_1,\ldots,x_n\rangle^2$, and describe the completion of the universal family.…

We generalise the analysis carried out in [arXiv:0710.5796], and find that our previous results can be extended beyond the case of SL(N,C). In particular, we show that an equivalence--at the level of the holomorphic chiral algebra--between…

We study the local cohomology modules H^i_B(R) for a reduced monomial ideal B in a polynomial ring R=k[X_1,...,X_n]. We consider a grading on R which is coarser than the Z^n-grading such that each component of H^i_B(R) is finite dimensional…

We compute the cohomological Hall algebra of zero-dimensional sheaves on an arbitrary smooth quasi-projective surface $S$ with pure cohomology, deriving an explicit presentation by generators and relations. When $S$ has trivial canonical…

Given a partial action $\alpha$ of a groupoid $G$ on a ring $R$, we study the associated partial skew groupoid ring $R \rtimes_{\alpha} G$, which carries a natural $G$-grading. We show that there is a one-to-one correspondence between the…

In this paper, we investigate the properties of $A$-coherent and $A$-quasi-coherent sheaves within the framework of algebraic geometry over non-algebraically closed fields. We define an $\mathcal{O}_X$-module to be $A$-coherent (resp.…

(Makes a Gamma-acylic coherent resolution of a coherent sheaf on a projection scheme.)

Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete…

In this paper, given a smooth proper scheme X over a p-adic dvr and a p-power torsion etale local system L on it, we study a family of sheaves associated to the cohomology of local relative (Phi-Gamma)-modules of L and their cohomology. As…

In this paper, we study the second adjoint cohomology of the compexification of the real conformal Galilei algebras \(\mathfrak{cga}_\ell(d,\mathbb{R})\) and their central extensions. These algebras are non-semisimple Lie algebras that…

Let $K$ be the fraction field of a two-dimensional henselian, excellent, equi-characteristic local domain. We prove a local-global principle for Galois cohomology with finite coefficients over $K$. We use classical machinery from \'etale…

The Gerstenhaber and Schack cohomology comparison theorem asserts that there is a cochain equivalence between the Hochschild complex of a certain algebra and the usual singular cochain complex of a space. We show that this comparison…