Let $f: X\rightarrow S$ be a faithful affine map. In this article we construct a group homomorphism $\theta_{{fppf}}: \text{Br}(f) \longrightarrow H^1_{{fppf}}\!\left(S, (f_*\mathcal{O}_X^\times / \mathcal{O}_S^\times)_{{fppf}}\right)$, extending the formerly defined morphism over an \'etale site $\theta_{et}$. In doing so, we eliminate the characteristic constraint previously found in the relative version of Kummer's exact sequence. Furthermore, given a finite subintegral extension of noetherian rings $A \hookrightarrow B$, we show that all the $fppf$ cohomology groups, $H^i_{fppf}(Spec(A),\mu^f_n); \;\forall i\geq 0$ vanish whenever $n$ does not divide the characteristic of $A$.
Let $X=\mathbb{P}^3$ and let \[ \alpha_n=(0,1,-\tfrac12,\tfrac16-n)\in H^{\mathrm{even}}(X,\mathbb{Q}) \] with respect to the basis $1,H,H^2,H^3$, where $H=c_1(\mathcal{O}_X(1))$. We prove that every Gieseker semistable sheaf on $X$ with Chern character $\alpha_n$ is stable and uniquely of the form $\iota_{P*}\mathcal{...
R. Anderson· Journal of Geometry and Phys...· 0 citations
We define a derived stack $\mathscr{Rep}_n(X)$ which generalizes the assignment $A\leadsto \operatorname{Rep}_n(A)$ to an algebra of its derived $GL_n$-representation variety of arXiv:1112.1449 from algebras $A$ to perfect stacks $X$ over characteristic 0 fields. In the case of a quasi-projective classical scheme $X$,...
Let $\mathcal C=(f)$ be a $\lambda$-constacyclic code over $\mathbb F_q$, where $f(X)$ is a monic factor of $X^N-\lambda$ with nonzero constant term. We introduce the support period $\operatorname{sp}(f)$ of $f(X)$, and define its support-primitive core $f_{\mathrm{sp}}(X)$ as the unique support-primitive polynomial sa...
Let $f$ be a regular endomorphism of $\mathbb{A}_{\mathbb{C}}^N$ of algebraic degree $d$ and let $f_{\infty}$ be the induced endomorphism of the infinity hyperplane $H_{\infty}$. Suppose that for every periodic point $x_0\in H_{\infty}(\mathbb{C})$ of period $n_0$, the geometric mean of the multiplicities $e_{f_{\infty...
We establish a Grothendieck six-functor formalism for Kummer \'etale cohomology including Poincar\'e duality for every separated vertical exact log smooth morphism of noetherian fs log schemes $f\colon X\rightarrow S$ when the coefficient ring $\Lambda$ is killed by an integer invertible on $S$. This is done via log \'...
We show that von Neumann algebras of fundamental groups of closed orientable surfaces of genus $g\geq2$ are free group factors on $2g-1$generators. The key technical ingredient involves a proof that the element $w=ABA^{-1}B^{-1}$ of the free group $\mathbb{F}_{2}=\langle A,B\rangle$ is freely complemented in the group...
Dima Shlyakhtenko· 2 citations· ⚡1
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
