Moduli schemes of rank one azumaya modules
WebLet A be an Azumaya algebra over a smooth projective variety X or more generally, a torsion free coherent sheaf of algebras over X whose generic fiber is a central simple algebra. We show that generically simple torsion free A-module sheaves have a projective coarse moduli scheme; it is smooth and even symplectic if X is an abelian or K3 surface … WebThen we study the moduli scheme of torsion free 𝓐-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the …
Moduli schemes of rank one azumaya modules
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Webstudy moduli schemes of sheaves generically of rank one on a noncommutative Enriques surface. Many of the results in the last section are noncommutative analogues of results … http://www.neverendingbooks.org/reading-backlog
WebIn this note we prove that the moduli space of torsion-free modules of rank one over an Azumaya algebra on a K3 surface is an irreducible symplectic variety deformation … Web4 nov. 2004 · Download a PDF of the paper titled Moduli schemes of rank one Azumaya modules, by Norbert Hoffmann and 1 other authors Download PDF Abstract: Let A be a …
WebSchmidt-Azumaya theorem [2], using results of Crawley and Jónsson [3]. We apply this result to obtain a number of results on direct sums of modules, including generalizations of Kaplansky's theorem [4] that a projective module over a logical ring is free. 1. The exchange property. A module M (over an associative ring WebConsider a projective module P of finite type over a commutative ring A. It corresponds to a locally free sheaf F over X = S p e c ( A). The rank of F at the prime ideal p is that of the …
WebWe will also need the notion of modules over an Azumaya algebra. Definition 1.10. Let X be any scheme and let A be an Azumaya algebra over X. A sheaf of OX-modules M is called an Azumaya module if it has the structure of a locally projective left A-module. An Azumaya module is called an Azumaya line bundle, if Mη is
WebLemma IV.1.11] Corollary 2.6. Let Abe a free module of rank lover (R;m) and let k= R=m, then the following are equivalent: Ais Azumaya over R A kis a CSA over k A k˘=M n(k) In particular l= n2 for some n2N Corollary 2.7. The tensor product of two Azumaya algebras is an Azu-maya algebra. M n(R) is Azumaya over R We now state the main result of ... snap benefits customer service nyWebOF MODULES R. B. WARFIELD, JR. In this note we prove a strengthened form of the well-known Krull-Schmidt-Azumaya theorem [2], using results of Crawley and Jonsson [3]. We apply this result to obtain a number of results on direct stims of modules, including generalizations of Kaplansky's theorem [4] that a projective module over a logical ring ... roach cigarette buttWeb10 nov. 2015 · In this note we prove that the moduli space of torsion-free modules of rank one over an Azumaya algebra on a K3-surface is an irreducible symplectic variety … roach chiropracticWeb14 apr. 2012 · Quite generally, the moduli schemes $M^r (\fa)$ encode essential parts of the arithmetic of $A$ and $K$, as will be demonstrated by the examples below. Applications. Explicit Abelian class field theory of $K$. Adjoining torsion points of rank-one Drinfel'd modules results in Abelian extensions of the base field. roach chirpWeb2 apr. 2008 · Abstract. The aim of this paper is to construct the parabolic version of the Donaldson-Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algebraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non-emptiness of the moduli space of parabolic stable … snap benefits cuyahoga countyWeb9 sep. 2024 · Moduli schemes of generically simple Azumaya modules Article Dec 2004 Norbert Hoffmann Ulrich Stuhler View Show abstract Germany E-mail address: … roach chocolateWebLet X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra A on X. Then we study the moduli scheme of torsion free A-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated … snap benefits customer service number ny