Selmer groups for elliptic curves in Z_l^d-extensions of function fields of characteristic p

Let $F$ be a function field of characteristic $p>0$, \F/F a Galois extension with Gal(\F/F)\simeq \Z_l^d (for some prime $l\neq p$) and $E/F$ a non-isotrivial elliptic curve. We study the behaviour of Selmer groups $Sel_E(L)_r$ ($r$ any prime) as $L$ varies through the subextensions of \F via appropriate versions of Mazur's Control Theorem. As a consequence we prove that Sel_E(\F)_r is a cofinitely generated (in some cases cotorsion) \Z_r[[Gal(\F/F)]]-module.Comment: Final version to appear in Annales de l'Institut Fourie

Spoken Thesaurus: Sorrow

The Hindi Thesaurus addresses such questions in a series of lively, unscripted Hindi-medium conversations about groups of words of related meaning. Concentrating on selected mainstream words and phrases, we help you to broaden your active vocabulary by encountering styles of language appropriate for everyday speech. The conversations are between Rupert Snell (Hindi teacher and perpetual Hindi learner) and Neha Ladha (mother-tongue speaker of Hindi). Glossaries for each podcast can be read online or downloaded in PDF format. (Length: 7:49)Asian Studie

Characteristic ideals and Selmer groups

Let $A$ be an abelian variety defined over a global field $F$ of positive characteristic $p$ and let \calf/F be a $\Z_p^{\N}$-extension, unramified outside a finite set of places of $F$. Assuming that all ramified places are totally ramified, we define a pro-characteristic ideal associated to the Pontrjagin dual of the $p$-primary Selmer group of $A$, in order to formulate an Iwasawa Main Conjecture for the non-noetherian commutative Iwasawa algebra \Z_p[[\Gal(\calf/F)]] (which we also prove for a constant abelian variety). To do this we first show the relation between the characteristic ideals of duals of Selmer groups for a $\Z_p^d$-extension \calf_d/F and for any $\Z_p^{d-1}$-extension contained in \calf_d\,, and then use a limit process.Comment: 10 pages, version updated to be compatible with the modifications of arXiv:1310.0680 [math.NT

Characteristic ideals and Iwasawa theory

Let \L be a non-noetherian Krull domain which is the inverse limit of noetherian Krull domains \L_d and let $M$ be a finitely generated \L-module which is the inverse limit of \L_d-modules $M_d\,$. Under certain hypotheses on the rings \L_d and on the modules $M_d\,$, we define a pro-characteristic ideal for $M$ in \L, which should play the role of the usual characteristic ideals for finitely generated modules over noetherian Krull domains. We apply this to the study of Iwasawa modules (in particular of class groups) in a non-noetherian Iwasawa algebra \Z_p[[\Gal(\calf/F)]], where $F$ is a function field of characteristic $p$ and \Gal(\calf/F)\simeq\Z_p^\infty.Comment: 15 pages, substantial chenges in exposition, new section 2.

La iglesia de San Paolo en Rho (Milan, 1978/90). Luigi Leoni y padre Costantino Ruggeri

Analisi di un'architettura liturgica contemporanea, secondo una griglia di indagine che privilegia i temi di storia della liturgia, della comunità e del vissuto ecclesiali, letti sulla lunga durata del cantiere e dell'adattamento dell'edificio dopo il suo completament

Tempio e persona: antropomorfismo e cristocentrismo nell'architettura cristiana (secoli XII-XVI)

La ricerca si inserisce in un progetto di ricerca interdisciplinare sul rapporto tra persona e luoghi di culto nelle diverse religioni, sulle relazioni tra antropologie e architetture religiose. Il saggio sviluppa il tema dell'architettura cristiana, analizzando la trattatistica architettonica e teologica dei secoli compresi tra il Duecento e la Controriforma, affrontando in particolare l'utilizzo della pianta antropomorfica (a croce, essenzialmente), letto nelle chiavi di lettura teologica e liturgica. Il riferimento cristologico implicito nell'uso della forma antropomorfica e cruciforme viene progressivamente ripensato e abbandonato nel passaggio alla cultura teologica e architettonica controriformista, in cui alla metafora fisica della Chiesa interpretata come corpo (antropomorfo) di Cristo subentra una rinnovata attenzione teologica al Corpo di Cristo inteso come Eucaristia,tema attorno a cui gravita la rinnovata architettura post-tridentin

The church of San Paolo in Rho (Milan, 1978/90)

[Resumen] Las superfi cies sinuosas de la iglesia de San Paolo ofrecen una doble cara. Hacia el interior, responden a la articulación de la acción litúrgica; hacia el exterior, se insertan en la trama verde del paisaje periurbano, en el límite entre la ciudad y el contexto rural. Espacio litúrgico y ambiente externo establecen, por tanto, una fuerte relación dinámica: una correspondencia física (de reciprocidad volumétrica entre las paredes cóncavas y convexas), pero sobre todo, una correspondencia visual y lumínica, gracias a las vidrieras polícromas que permiten una dialéctica siempre diversa entre los volúmenes marmóreos de los polos litúrgicos, las superfi cies blancas que los acogen y la luz coloreada que los ilumina.[Abstract] Th e sinuous surfaces of the church of San Paolo off er a double-sided. Inland, respond to the articulation of the liturgical action, outwards are inserted into the weft green suburban landscape, at the boundary between the city and the rural context. Liturgical space and external environment provide therefore a strong dynamic relationship: a physical map (volumetric reciprocity between the concave and convex walls), but above all a visual and lightly correspondence, due to the polychrome glass windows that allow a dialectic always diff erent between the marble volumes of liturgical poles, white surfaces that host and colored lights that bathes them

Tra fondazioni non riuscite e rischi di abbandono: i casi di Villanova e Villabona presso l'attuale Moretta

Fascicolo monografico "Villaggi scomparsi e borghi nuovi nel Piemonte medievale", a cura di Rinaldo Comba e Riccardo Ra

Calling ‘Values’ by ‘Name’. Historical Analysis and Critical Discernment for the Interpretation and Regeneration of Underused Religious Heritage

The debate on the reuse of religious cultural heritage necessarily revolves around shared meanings and values: heritage communities will be able to discuss and design a future for their religious properties only if they share common languages and criteria of discernment. Nonetheless, there is a risk that a generic call to common ‘values’ will continue to be superficial, rhetorical or ‘appeasing’. Conversely, the dramatic nature of the subject calls for rigorous assessment and selection criteria, the ability to make decisions – including painful ones – without euphemisms, and the courage to embark on ambitious paths of social and architectural regeneration. As a theoretical contribution to the debate, a taxonomy of values is proposed here, based on a process-centred historical approach, founded on the investigation of the ‘formative processes’ behind heritage and its multiple meanings. The aim is to begin to build a shared lexicon – mainly in the field of the relationship between history, memory, and society – capable of accompanying innovative narratives and critical assessment tools. The possibility of assigning specific ‘names’ to ‘values’ will allow a positive interaction between the processes of community discernment and external expertise: in this perspective, each reuse will be considered an additional and creative step, incorporated in a long process of adaptation and resilience, based on a historical sequence of different and coexisting values