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Academic literature on the topic 'Shimura varietie'

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Published: 9 March 2023
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Journal articles on the topic "Shimura varietie"

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Scholze, Peter. "Perfectoid Shimura varieties." Japanese Journal of Mathematics 11, no. 1 (November 17, 2015): 15–32. http://dx.doi.org/10.1007/s11537-016-1484-6.

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Giacomini, Michele. "Holomorphic curves in Shimura varieties." Archiv der Mathematik 111, no. 4 (August 17, 2018): 379–88. http://dx.doi.org/10.1007/s00013-018-1227-4.

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Abstract We prove a hyperbolic analogue of the Bloch–Ochiai theorem about the Zariski closure of holomorphic curves in abelian varieties. We consider the case of non compact Shimura varieties completing the proof of the result for all Shimura varieties. The statement which we consider here was first formulated and proven by Ullmo and Yafaev for compact Shimura varieties.
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Gao, Ziyang. "Towards the Andre–Oort conjecture for mixed Shimura varieties: The Ax–Lindemann theorem and lower bounds for Galois orbits of special points." Journal für die reine und angewandte Mathematik (Crelles Journal) 2017, no. 732 (November 1, 2017): 85–146. http://dx.doi.org/10.1515/crelle-2014-0127.

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Abstract We prove in this paper the Ax–Lindemann–Weierstraß theorem for all mixed Shimura varieties and discuss the lower bounds for Galois orbits of special points of mixed Shimura varieties. In particular, we reprove a result of Silverberg [57] in a different approach. Then combining these results we prove the André–Oort conjecture unconditionally for any mixed Shimura variety whose pure part is a subvariety of {\mathcal{A}_{6}^{n}} and under the Generalized Riemann Hypothesis for all mixed Shimura varieties of abelian type.
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Fargues, Laurent, Ulrich Görtz, Eva Viehmann, and Torsten Wedhorn. "Reductions of Shimura Varieties." Oberwolfach Reports 9, no. 3 (2012): 1961–2011. http://dx.doi.org/10.4171/owr/2012/32.

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Fargues, Laurent, Ulrich Görtz, Eva Viehmann, and Torsten Wedhorn. "Reductions of Shimura Varieties." Oberwolfach Reports 12, no. 3 (2015): 2265–328. http://dx.doi.org/10.4171/owr/2015/39.

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Fargues, Laurent, Ulrich Görtz, Eva Viehmann, and Torsten Wedhorn. "Arithmetic of Shimura Varieties." Oberwolfach Reports 16, no. 1 (February 26, 2020): 65–131. http://dx.doi.org/10.4171/owr/2019/2.

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Edixhoven, Bas, and Andrei Yafaev. "Subvarieties of Shimura varieties." Annals of Mathematics 157, no. 2 (March 1, 2003): 621–45. http://dx.doi.org/10.4007/annals.2003.157.621.

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Milne, J. S. "Descent for Shimura varieties." Michigan Mathematical Journal 46, no. 1 (May 1999): 203–8. http://dx.doi.org/10.1307/mmj/1030132370.

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Boyer, Pascal. "Conjecture de monodromie-poids pour quelques variétés de Shimura unitaires." Compositio Mathematica 146, no. 2 (January 26, 2010): 367–403. http://dx.doi.org/10.1112/s0010437x09004588.

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AbstractIn Boyer [Monodromy of perverse sheaves on vanishing cycles on some Shimura varieties, Invent. Math. 177 (2009), 239–280 (in French)], a sheaf version of the monodromy-weight conjecture for some unitary Shimura varieties was proved by giving explicitly the monodromy filtration of the complex of vanishing cycles in terms of local systems introduced in Harris and Taylor [The geometry and cohomology of some simple Shimura varieties (Princeton University Press, Princeton, NJ, 2001)]. The main result of this paper is the cohomological version of the monodromy-weight conjecture for these Shimura varieties, which we prove by means of an explicit description of the groups of cohomology in terms of automorphic representations and the local Langlands correspondence.
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Shin, Sug Woo. "A stable trace formula for Igusa varieties." Journal of the Institute of Mathematics of Jussieu 9, no. 4 (March 23, 2010): 847–95. http://dx.doi.org/10.1017/s1474748010000046.

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AbstractIgusa varieties are smooth varieties in positive characteristic p which are closely related to Shimura varieties and Rapoport–Zink spaces. One motivation for studying Igusa varieties is to analyse the representations in the cohomology of Shimura varieties which may be ramified at p. The main purpose of this work is to stabilize the trace formula for the cohomology of Igusa varieties arising from a PEL datum of type (A) or (C). Our proof is unconditional thanks to the recent proof of the fundamental lemma by Ngô, Waldspurger and many others.An earlier work of Kottwitz, which inspired our work and proves the stable trace formula for the special fibres of PEL Shimura varieties with good reduction, provides an explicit way to stabilize terms at ∞. Stabilization away from p and ∞ is carried out by the usual Langlands–Shelstad transfer as in work of Kottwitz. The key point of our work is to develop an explicit method to handle the orbital integrals at p. Our approach has the technical advantage that we do not need to deal with twisted orbital integrals or the twisted fundamental lemma.One application of our formula, among others, is the computation of the arithmetic cohomology of some compact PEL-type Shimura varieties of type (A) with non-trivial endoscopy. This is worked out in a preprint of the author's entitled ‘Galois representations arising from some compact Shimura varieties’.
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Dissertations / Theses on the topic "Shimura varietie"

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GROSSELLI, GIAN PAOLO. "Shimura varieties in the Prym loci of Galois covers." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/356638.

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In questa tesi si studiano le sottovarietà di Shimura negli spazi di moduli delle varietà abeliane complesse. Queste sottovarietà derivano da famiglie di rivestimenti di Galois compatibili con un'azione di gruppo fissata sulla curva base tale che il quoziente della curva base per il gruppo è isomorfo alla retta proiettiva. Si da un criterio affinché l'immagine di queste famiglie tramite la mappa di Prym sia una sottovarietà speciale e, sfruttando il computer, si costruiscono numerose sottovarietà di Shimura contenute nei luoghi di Prym.
In this thesis we study Shimura subvarieties in the moduli space of complex abelian varieties. These subvarieties arise from families of Galois covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to the projective line. We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, we build several Shimura subvarieties contained in the Prym loci.
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Yafaev, Andrei. "Sous-varietes des varietes de shimura." Rennes 1, 2000. http://www.theses.fr/2000REN10151.

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Dans cette these on traite certains cas de la conjecture d'andre-oort qui affirme que les composantes irreductibles de l'adherence de zariski d'un ensemble de points speciaux dans une variete de shimura est une sousvariete de type hodge. Le premier resultat traite le cas des courbes dans un produit s 1 s 2 ou s 1 et s 2 sont des courbes de shimura associees aux algebres de quaternions indefines sur q. On demontre la conjecture d'andre-oort pour un tel produit en supposant l'hypothese de riemann generalisee. Le deuxieme resultat affirme qu'une courbe irreductible fermee dans une variete de shimura quelconque s contenant un ensemble infini de points qui sont dans une orbite de hecke est de type hodge. Ce resultat implique, via le travail de cohen, wolfart et wustholz, une conjecture sur la transcendence de valeurs de fonctions hypergeometriques.
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Pink, Richard. "Arithmetical compactification of mixed Shimura varieties." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/24807098.html.

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Ha, Eugene. "Quantum statistical mechanics of Shimura varieties." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980749964.

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Soylu, Cihan. "Special Cycles on GSpin Shimura Varieties:." Thesis, Boston College, 2017. http://hdl.handle.net/2345/bc-ir:107320.

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Thesis advisor: Ben Howard
The results in this dissertation are on the intersection behavior of certain special cycles on GSpin(n, 2) Shimura varieties for n > 1. In particular, we will determine when the intersection of the special cycles defined by a collection of special endomorphisms consists of isolated points in terms of the fundamental matrix of this collection. These generalize the corresponding results in the lower dimensional cases proved by Kudla and Rapoport
Thesis (PhD) — Boston College, 2017
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Chen, Ke. "Special subvarieties of mixed shimura varieties." Paris 11, 2009. http://www.theses.fr/2009PA112177.

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Cette thèse est dédiée à l'étude de la conjecture d'André-Oort pour les variétés de Shimura mixtes. On montre que dans une variété de Shimura mixte M définie par une donnée de Shimura mixte (P,Y), soient C un Q-tore dans P et Z une sous-variété fermée quelconque dans M, alors l'ensemble des sous-variétés C-spéciales maximales contenues dans Z est fini. La démonstration suit la stratégie de L. Clozel, E. Ullmo, et A. Yafaev dans le cas pure, qui dépend de la théorie de Ratner sur des propriétés ergodiques des flots unipotents sur des espaces homogénes. D'ailleurs, une minoration sur le degré de l'orbite sous Galois d'une sous-variété pure est montrée dans le cas mixte, adaptée du cas pure établi par E. Ullmo et A. Yafaev. Enfin, une version relative de la conjecture de Manin-Mumford est démontrée en caractéristique nul: soit A un S-schéma abélien en caractéristique nul, alors l'adhérence de Zariski d'une suite de sous-schémas de torsion dans A égale une réunion finie de sous-schémas de torsion
This thesis studies the André-Oort conjecture for mixed Shimura varieties. The main result is: let M be a mixed Shimura variety defined by a mixed Shimura datum (P,Y), C a fixed Q-torus of P, and Z an arbitrary closed subvariety in M, then the set of maximal C-special subvarieties of M contained in Z is finite. The proof follows the strategy applied by L. Clozel, E. Ullmo, and A. Yafaev in the pure case, which relies on Ratner's theory on ergodic properties of unipotent flows on homogeneous spaces. Besides, a minoration on the degree of the Galois orbit of a special subvariety is proved in the mixed case, adapted from the pure case established by E. Ullmo and A. Yafaev. Finally, a relative version of the Manin-Mumford conjecture is proved in characteristic zero: let A be an abelian S-scheme of characteristic zero, then the Zariski closure of a sequence of torsion subschemes in A remains a finite union of torsion subschemes
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Li, Hao. "Congruence relation for GSpin Shimura varieties:." Thesis, Boston College, 2021. http://hdl.handle.net/2345/bc-ir:109206.

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Thesis advisor: Benjamin Howard
I prove the Chai-Faltings version of the Eichler-Shimura congruence relation for simple GSpin Shimura varieties with hyperspecial level structures at a prime p
Thesis (PhD) — Boston College, 2021
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Fiori, Andrew. "Questions in the theory of orthogonal shimura varieties." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119536.

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We investigate a variety of questions in the theory of Shimura varieties of orthogonal type. Firstly we provide a general introduction in the theory of these spaces. Secondly, motivated by the problem of understanding the special points on Shimura varieties of orthogonal type we give a characterization of the maximal algebraic tori contained in orthogonal groups over an arbitrary number field. Finally, motivated by the problem of computing dimension formulas for spaces of modular forms, we compute local representation densities of lattices focusing specifically on those arising from Hermitian forms by transfer.
Le but de cette thèse est l'exploration d'une variété de questions sur les variétés de Shimura de type orthogonal. On commence par une introduction à la théorie de ces espaces. Àpres, dans le but de caractériser les points spéciauxsur les variétés de Shimura de type orthogonal, on décrit les tores algébriques maximaux dans les groupes orthogonaux. Finalement, dans le but d'obtenir des formules explicites pour la dimension des espaces de formes modulaires sur les variétés de Shimura de type orthogonal, on trouve des formules pour les densités locales des réseaux. On se concentre sur les réseaux qui proviennent de la restriction de formes Hermitiennes.
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Bultel, Oliver. "On the mod p-reduction of ordinary CM-points." Thesis, University of Oxford, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388853.

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Johansson, Hans Christian. "Classicality of overconvergent automorphic forms on some Shimura varieties." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/12897.

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This thesis consists of two parts. In Part 1 we study the rigid cohomology of the ordinary locus in some compact PEL Shimura varieties of type C with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent Hecke eigenforms, generalizing work of Coleman. In part 2 we compare the conjecture of Buzzard-Gee on the association of Galois representations to C-algebraic automorphic representations with the conjectural description of the cohomology of Shimura varieties due to Kottwitz, and the reciprocity law at infinity due to Arthur. This is done by extending Langlands's representation of the L-group associated with a Shimura datum to a representation of the C-group of Buzzard-Gee. The approach offers an explanation of the explicit Tate twist appearing in Kottwitz's description.
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Books on the topic "Shimura varietie"

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Fargues, Laurent. Variétés de Shimura, espaces de Rapoport-Zink et correspondances de Langlands locales. Paris: Société Mathématique de France, 2004.

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Benjamin, Howard, and Kudla Stephen S. 1950-, eds. Arithmetic divisors on orthogonal and unitary Shimura varieties. Paris: Société Mathématique de France, 2020.

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Hida, Haruzo. p-Adic Automorphic Forms on Shimura Varieties. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4684-9390-0.

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Dung, Nguyen Chi. Geometric pullback formula for unitary Shimura varieties. [New York, N.Y.?]: [publisher not identified], 2022.

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Atanasov, Stanislav Ivanov. Derived Hecke Operators on Unitary Shimura Varieties. [New York, N.Y.?]: [publisher not identified], 2022.

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Hida, Haruzo. p-Adic Automorphic Forms on Shimura Varieties. New York, NY: Springer New York, 2004.

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Harris, Michael. Boundary cohomology of Shimura varieties, III: Coherent cohomology on higher-rank boundary strata and applications to Hodge theory. Paris, France: Société Mathématique de France, 2001.

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Harris, Michael. Boundary cohomology of Shimura varieties, III: Coherent cohomology on higher-rank boundary strata and applications to Hodge theory. Paris, France: Société mathématique de France, 2001.

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On the cohomology of certain noncompact Shimura varieties. Princeton: Princeton University Press, 2010.

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Automorphic forms and Shimura varieties of PGSp (2). Singapore: World Scientific Pub., 2005.

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Book chapters on the topic "Shimura varietie"

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Hida, Haruzo. "Shimura Varieties." In Springer Monographs in Mathematics, 303–28. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4684-9390-0_7.

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Rotger, Victor. "Shimura Curves Embedded in Igusa’s Threefold." In Modular Curves and Abelian Varieties, 263–76. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7919-4_16.

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Gross, Benedict H. "Incoherent Definite Spaces and Shimura Varieties." In Simons Symposia, 187–215. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68506-5_5.

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Hida, Haruzo. "Modular Curves as Shimura Variety." In Springer Monographs in Mathematics, 281–334. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6657-4_7.

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Venkataramana, T. N. "Lefschetz Properties of Subvarieties of Shimura Varieties." In Current Trends in Number Theory, 265–70. Gurgaon: Hindustan Book Agency, 2002. http://dx.doi.org/10.1007/978-93-86279-09-5_24.

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Carlson, James A., and Carlos Simpson. "Shimura Varieties of Weight Two Hodge Structures." In Lecture Notes in Mathematics, 1–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077525.

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Burgos Gil, José Ignacio. "Chapter X: Arakelov Theory on Shimura Varieties." In Lecture Notes in Mathematics, 377–401. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-57559-5_11.

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Hida, Haruzo. "Invariants, Shimura Variety, and Hecke Algebra." In Springer Monographs in Mathematics, 83–144. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6657-4_3.

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Wedhorn, Torsten. "The Dimension of Oort Strata of Shimura Varieties of Pel-Type." In Moduli of Abelian Varieties, 441–71. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0_15.

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Rohde, Jan Christian. "An Introduction to Hodge Structures and Shimura Varieties." In Cyclic Coverings, Calabi-Yau Manifolds and Complex Multiplication, 11–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00639-5_2.

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Conference papers on the topic "Shimura varietie"

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PAPPAS, GEORGIOS. "ARITHMETIC MODELS FOR SHIMURA VARIETIES." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0059.

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Morel, Sophie. "The Intersection Complex as a Weight Truncation and an Application to Shimura Varieties." In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010). Published by Hindustan Book Agency (HBA), India. WSPC Distribute for All Markets Except in India, 2011. http://dx.doi.org/10.1142/9789814324359_0053.

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Reports on the topic "Shimura varietie"

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Blumwald, Eduardo, and Avi Sadka. Citric acid metabolism and mobilization in citrus fruit. United States Department of Agriculture, October 2007. http://dx.doi.org/10.32747/2007.7587732.bard.

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Accumulation of citric acid is a major determinant of maturity and fruit quality in citrus. Many citrus varieties accumulate citric acid in concentrations that exceed market desires, reducing grower income and consumer satisfaction. Citrate is accumulated in the vacuole of the juice sac cell, a process that requires both metabolic changes and transport across cellular membranes, in particular, the mitochondrial and the vacuolar (tonoplast) membranes. Although the accumulation of citrate in the vacuoles of juice cells has been clearly demonstrated, the mechanisms for vacuolar citrate homeostasis and the components controlling citrate metabolism and transport are still unknown. Previous results in the PIs’ laboratories have indicated that the expression of a large number of a large number of proteins is enhanced during fruit development, and that the regulation of sugar and acid content in fruits is correlated with the differential expression of a large number of proteins that could play significant roles in fruit acid accumulation and/or regulation of acid content. The objectives of this proposal are: i) the characterization of transporters that mediate the transport of citrate and determine their role in uptake/retrieval in juice sac cells; ii) the study of citric acid metabolism, in particular the effect of arsenical compounds affecting citric acid levels and mobilization; and iii) the development of a citrus fruit proteomics platform to identify and characterize key processes associated with fruit development in general and sugar and acid accumulation in particular. The understanding of the cellular processes that determine the citrate content in citrus fruits will contribute to the development of tools aimed at the enhancement of citrus fruit quality. Our efforts resulted in the identification, cloning and characterization of CsCit1 (Citrus sinensis citrate transporter 1) from Navel oranges (Citrus sinesins cv Washington). Higher levels of CsCit1 transcripts were detected at later stages of fruit development that coincided with the decrease in the juice cell citrate concentrations (Shimada et al., 2006). Our functional analysis revealed that CsCit1 mediates the vacuolar efflux of citrate and that the CsCit1 operates as an electroneutral 1CitrateH2-/2H+ symporter. Our results supported the notion that it is the low permeable citrateH2 - the anion that establishes the buffer capacity of the fruit and determines its overall acidity. On the other hand, it is the more permeable form, CitrateH2-, which is being exported into the cytosol during maturation and controls the citrate catabolism in the juice cells. Our Mass-Spectrometry-based proteomics efforts (using MALDI-TOF-TOF and LC2- MS-MS) identified a large number of fruit juice sac cell proteins and established comparisons of protein synthesis patterns during fruit development. So far, we have identified over 1,500 fruit specific proteins that play roles in sugar metabolism, citric acid cycle, signaling, transport, processing, etc., and organized these proteins into 84 known biosynthetic pathways (Katz et al. 2007). This data is now being integrated in a public database and will serve as a valuable tool for the scientific community in general and fruit scientists in particular. Using molecular, biochemical and physiological approaches we have identified factors affecting the activity of aconitase, which catalyze the first step of citrate catabolism (Shlizerman et al., 2007). Iron limitation specifically reduced the activity of the cytosolic, but not the mitochondrial, aconitase, increasing the acid level in the fruit. Citramalate (a natural compound in the juice) also inhibits the activity of aconitase, and it plays a major role in acid accumulation during the first half of fruit development. On the other hand, arsenite induced increased levels of aconitase, decreasing fruit acidity. We have initiated studies aimed at the identification of the citramalate biosynthetic pathway and the role(s) of isopropylmalate synthase in this pathway. These studies, especially those involved aconitase inhibition by citramalate, are aimed at the development of tools to control fruit acidity, particularly in those cases where acid level declines below the desired threshold. Our work has significant implications both scientifically and practically and is directly aimed at the improvement of fruit quality through the improvement of existing pre- and post-harvest fruit treatments.
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