We introduce the volume function for C-hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef C-hermitian invertible sheaf. We also give another applications, for example, a generalized Hodge ...

We show, at the prime 2, that Picard group of invertible modules over $E_n^{hC_2}$ is cyclic. Here, $E_n$ height $n$ Lubin--Tate spectrum and its $C_2$-action induced from formal inverse associated law. further show Gross--Hopkins self-dual determine exact shift. Our results generalize well-known when $n = 1$.

Several applications in communication, control, and learning require approximating target distributions to within small informational divergence. The additional requirement of invertibility usually leads using encoders that are one-to-one mappings, also known as distribution matchers. However, even the best have divergences grow logarithmically with block length. To overcome this limitation, an...

For two central Drazin invertible elements a and b of ring, we first prove that + is under the condition ab = 0. Then establish relation between invertibility 1 acb, when a2b aba b2a bab hold, also ba valid. When are group elements, additive properties inverses studied abbc baac.