Adic Approximation of Complexes, and Multiplicities
نویسندگان
چکیده
In [2, Section 1.6] Peskine and Szpiro prove a theorem on adic approximations of finite free resolutions over local rings which, together with M. Artin's Approximation Theorem [1], allows them to "descend" modules of finite projective dimension over the completions of certain local rings to modules of finite projective dimension over finite etale extensions of those rings. In this note we will prove a more general result, which deals with the change in homology under an adic approximation of any complex of finitely generated modules over a noetherian ring, and which allows one to descend not only modules of finite projective dimension, but also the Euler characteristic or intersection multiplicity of two such modules. Henceforth, R will be a commutative noetherian ring, and J will be an ideal in the (Jacobson) radical of R. If
منابع مشابه
Geometric and Electronic Structures of Vanadium Sub-nano Clusters, Vn (n = 2-5), and their Adsorption Complexes with CO and O2 Ligands: A DFT-NBO Study
In this study, electronic structures of ground state of pure vanadium sub-nano clusters, Vn (n=2-5), and their interactions with small ligands for example CO and triplet O2 molecules are investigated by using density functional theory (DFT) calibration at the mPWPW91/QZVP level of theory. The favorable orientations of these ligands in interaction with pure vanadium sub-nano clusters were determ...
متن کاملp-adic Shearlets
The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.
متن کاملThe Fontaine-mazur Conjecture for Gl2
Introduction 641 1. Breuil-Mézard conjecture and the p-adic local Langlands 644 (1.1) The Breuil-Mézard conjecture 644 (1.2) Review of Colmez’s functor 647 (1.3) Hilbert-Samuel multiplicities 650 (1.4) Representations and pseudo-representations 653 (1.5) GL2(Qp)-representations mod p. 657 (1.6) Local patching and multiplicities 661 (1.7) From pseudo-representations to representations 669 2. Mod...
متن کاملPositive-additive functional equations in non-Archimedean $C^*$-algebras
Hensel [K. Hensel, Deutsch. Math. Verein, {6} (1897), 83-88.] discovered the $p$-adic number as a number theoretical analogue of power series in complex analysis. Fix a prime number $p$. for any nonzero rational number $x$, there exists a unique integer $n_x inmathbb{Z}$ such that $x = frac{a}{b}p^{n_x}$, where $a$ and $b$ are integers not divisible by $p$. Then $|x...
متن کاملThe Jordan-Hölder series for nearby cycles on some Shimura varieties and affine flag varieties
We study the Jordan-Hölder series for nearby cycles on certain Shimura varieties and Rapoport-Zink local models, and on finite-dimensional pieces of Beilinson’s deformation of the affine Grassmannian to the affine flag variety (and their p-adic analogues). We give a formula for the multiplicities of irreducible constituents in terms of certain cohomology groups, and we also provide an algorithm...
متن کامل