We prove in this note that the global geometric theta lifting for the pair (H,G) is compatible with the Whittaker normalization, where (H,G) = (SO2n, Sp2n), (Sp2n, SO2n+2), or (GLn, GLn+1). More precisely, let k be an algebraically closed field of characteristic p > 2. Let X be a smooth projective connected curve over k. For a stack S write D(S) for the derived category of étale constructible Q̄...

Pink has given a qualitative answer to the Mumford-Tate conjecture for Drinfeld modules in 90s. He showed that image of v-adic Galois representation is v-adically open motivic group any prime v. In contrast this result, we provide family uniformizable Anderson t-modules which representations their t-adic Tate-modules are "far from" having t-adically groups. Nevertheless, still Zariski-dense acc...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

The article considers an approach to determining the labor-intensiveness and duration of consolidation processes during installation structural blocks covering, which is caused by atypical technological solutions. relevance this work need for a qualitative analysis methods calculating labor intensity when justifying making decisions regarding organization mechanization assembly processes.
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In this article we show that all periods of uniformizable $t$-modules (resp. their coordinates) can be obtained via specializing a rigid analytic trivialization related dual $t$-motive at $t=\theta$. The proof is even constructive. central object in the construction subset $H$ Tate algebra points $E$ which turns out to isomorphic period lattice kind generating series one direction and residues ...

The theory of Drinfeld modules was initially developed to transport the classical ideas of lattices and exponential functions to the function field setting in positive characteristic. This impulse manifested itself in work of L. Carlitz [9], who investigated explicit class field theory for Fq(θ) and defined the later named Carlitz module, which serves as the analogue of the multiplicative group...

We generalize the results of [CHT08] and [Tay08] by proving modularity lifting theorems for ordinary l-adic Galois representations of any dimension of a CM or totally real number field F . The main theorems are obtained by establishing an R = T theorem over a Hida family. A key part of the proof is to construct appropriate ordinary lifting rings at the primes dividing l and to determine their i...