1,721,066 research outputs found
Stabilization in non-abelian Iwasawa theory
No full textLet K/k be a Z_p-extension of a number field k, and denote by k_n its layers. We prove some stabilization properties for the orders and the p-ranks of the higher Iwasawa modules arising from the lower central series of the Galois group of the maximal unramified pro-p-extension of K (resp. of the k_n)
Control theorems for l-adic Lie extensions of global function fields
Full text linkLet F be a global function field of characteristic p>0, K/F an l-adic Lie extension unramified outside a finite set of places S and A/F an abelian variety. We study Sel_A(K)_l^ee (the Pontrjagin dual of the Selmer group) and (under some mild hypotheses) prove that it is a finitely generated Z_l[[Gal(K/F)]]-module via generalizations of Mazur's Control Theorem. If Gal(K/F) has no elements of order l and contains a closed normal subgroup H such that Gal(K/F)/H simeq Z_l, we are able to give sufficient conditions for Sel_A(K)_l^ee to be finitely generated as Z_l[[H]]-module and, consequently, a torsion Z_l[[Gal(K/F)]]-module. We deal with both cases l
eq p and l=p
Extensions of the p-adic fields generated by the roots of a single polynomial in two variables
No full textAnalysis of the hands in egocentric vision: A survey
Full text linkEgocentric vision (a.k.a. first-person vision - FPV) applications have
thrived over the past few years, thanks to the availability of affordable
wearable cameras and large annotated datasets. The position of the wearable
camera (usually mounted on the head) allows recording exactly what the camera
wearers have in front of them, in particular hands and manipulated objects.
This intrinsic advantage enables the study of the hands from multiple
perspectives: localizing hands and their parts within the images; understanding
what actions and activities the hands are involved in; and developing
human-computer interfaces that rely on hand gestures. In this survey, we review
the literature that focuses on the hands using egocentric vision, categorizing
the existing approaches into: localization (where are the hands or parts of
them?); interpretation (what are the hands doing?); and application (e.g.,
systems that used egocentric hand cues for solving a specific problem).
Moreover, a list of the most prominent datasets with hand-based annotations is
provided
Hecke operators and Drinfeld cusp forms of level t
Full text linkWe use a linear algebra interpretation of the action of Hecke operators on Drinfeld cusp forms to prove that, when the dimension of the C_\infty-vector space S_{k,m}(GL_2(F_q[t])) is one, the operator T_t is injective on S_{k,m}(GL_2(F_q[t])) and S_{k,m}(Γ_0(t)) is direct sum of oldforms and newforms
Greenberg's conjecture and capitulation in Zpd-extensions
No full textAbstractLet p be an odd prime. Let k be an algebraic number field and let k˜ be the compositum of all the Zp-extensions of k, so that Gal(k˜/k)≃Zpd for some finite d. We shall consider fields k with Gal(k/Q)≃(Z/2Z)n. Building on known results for quadratic fields, we shall show that the Galois group of the maximal abelian unramified pro-p-extension of k˜ is pseudo-null for several such k's, thus confirming a conjecture of Greenberg. Moreover we shall see that pseudo-nullity can be achieved quite early, namely in a Zp2-extension, and explain the consequences of this on the capitulation of ideals in such extensions
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