Projective moduleRankIntegral group ringLet P be a nonzero projective module over an integral group ring. We consider the question of whether the rank of P is necessarily positive.doi:10.1007/s00013-024-02081-yJohnson, F.E.A.Department of Mathematics, University College London, London, UK...
For an arbitrary R the authors construct a right self-injective regular ring V as being the ring of endomorphisms of the pure-injective envelope of the module R R modulo its Jacobson radical, and a ring homomorphism R→V. Using this, they prove that there exists a ring homomorphism of R...
be the projective space of dimension N over an algebraically closed field k of characteristic 0. If F⊆PN is an n-dimensional projective variety, i.e. an integral connected closed subscheme, we set OF(h):=OPN(1)⊗OF. We say that F ...
The equivalence is implemented by the Heisenberg module based on the (projective) Heisenberg representation of W. The critical compatibility condition for the two operator valued inner products on the bimodule reduces to the Poisson transformation in this case. In the local theta correspondence set-...
On the genus and Hartshorne-Rao module of projective curves The first main result is a so-called Restriction Theorem. It says that a non-degenerate curve of degreeinover a field of characteristic zero has a ... Nadia,Chiarli,Silvio,... - 《Mathematische Zeitschrift》 被引量: 50发表: 1998...
Two special examples of rank-like functions, emanating from the isomorphism classes of the finitely generated protective modules are examined, and it is shown that a simple unit-regular ring admits a metrizable topological ring structure, induced by the isomorphism classes of its projective modules....
First, the sum of the nonprojective direct summands of the representation, i.e., its core, is determined explicitly by local data given by the fixed point structure of the group acting on the curve. As a corollary, we derive a congruence formula for the p-rank. Secondly, t he ...
local ring R, a free resolution P of a non-zero R-module of finite length and finite projective dimension should satisfy rank R P n ≥ dimR n for each n; see [5], [16]. The Rank Inequality is proved in Section 5. The Class Inequality is established in Section 4, via a ver...
In Sect. 2, we set up basic definitions concerning projective modules over a Dedekind domain. In Sect. 3 and 4, respectively, we generalize to Dedekind base rings two classical parametrizations, namely of quadratic algebras over and of their ideals. In Sect. 5, we prove Bhargava’s ...
We see that the tempered theta correspondence, in the equal rank set-up, is simply the restriction of an equivalence of categories of representations of two C∗-algebras to the irreducible objects. As such it is functorial. Moreover, as it is implemented by an equivalence bimodule, it ...