Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most ...recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and give a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time. The book concludes with a comprehensive bibliography. It is destined to be a definitive reference on modern diophantine geometry, bringing a new standard of rigor and elegance to the field.
Abstract
In previous work, we have introduced δ-forms on the Berkovich analytification of an algebraic variety in order to study smooth or formal metrics via their associated Chern δ-forms. In this ...paper, we investigate positivity properties of δ-forms and δ-currents. This leads to various plurisubharmonicity notions for continuous metrics on line bundles. In the case of a formal metric, we show that many of these positivity notions are equivalent to Zhang’s semipositivity. For piecewise smooth metrics, we prove that plurisubharmonicity can be tested on tropical charts in terms of convex geometry. We apply this to smooth metrics, to canonical metrics on abelian varieties and to toric metrics on toric varieties.
We prove the Bogomolov conjecture for a totally degenerate abelian variety A over a function field. We adapt Zhang's proof of the number field case replacing the complex analytic tools by tropical ...analytic geometry. A key step is the tropical equidistribution theorem for A at the totally degenerate place v. As a corollary, we obtain finiteness of torsion points with coordinates in the maximal unramified algebraic extension over v. PUBLICATION ABSTRACT
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
For a closed d-dimensional subvariety X of an abelian variety A and a canonically metrized line bundle L on A, Chambert-Loir has introduced measures c1(L∣X)∧d on the Berkovich analytic space ...associated to A with respect to the discrete valuation of the ground field. In this paper, we give an explicit description of these canonical measures in terms of convex geometry. We use a generalization of the tropicalization related to the Raynaud extension of A and Mumford’s construction. The results have applications to the equidistribution of small points.
Cadophora species are reported from grapevine (Vitis vinifera L.) in California, South Africa, Spain, Uruguay, and Canada. Frequent isolation from vines co-infected with the Esca pathogens (Togninia ...minima and Phaeomoniella chlamydospora), and confirmation of its ability to cause wood lesions/discoloration in pathogenicity tests, suggest that C. luteo-olivacea is part of the trunk pathogen complex. In North America, little is known regarding the diversity, geographic distribution, and roles of Cadophora species as trunk pathogens. Accordingly, we characterized 37 Cadophora isolates from ten US states and two Canadian provinces, based on molecular and morphological comparisons, and pathogenicity. Phylogenetic analysis of three loci (ITS, translation elongation factor 1-alpha (TEF1-α) and beta-tubulin (BT)) distinguished two known species (C. luteo-olivacea and Cadophora melinii) and three newly-described species (Cadophora orientoamericana, Cadophora novi-eboraci, and Cadophora spadicis). C. orientoamericana, C. novi-eboraci, and C. spadicis were restricted to the northeastern US, whereas C. luteo-olivacea was only recovered from California. C. melinii was present in California and Ontario, Canada. Morphological characterization was less informative, due to significant overlap in dimensions of conidia, hyphae, conidiophores, and conidiogenous cells. Pathogenicity tests confirmed the presence of wood lesions after 24 m, suggesting that Cadophora species may have a role as grapevine trunk pathogens.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
Cultivars of European grapevine, Vitis vinifera, show varying levels of susceptibility to Eutypa dieback and Esca, in terms of foliar symptoms. However, little is known regarding cultivar ...susceptibility of their woody tissues to canker formation. Accordingly, we evaluated the relative susceptibility of V. vinifera cultivars ('Cabernet Franc', 'Cabernet Sauvignon', 'Chardonnay', 'Merlot', 'Riesling', 'Petite Syrah', and 'Thompson Seedless') and species or interspecific hybrids of North American Vitis (Vitis hybrid 'Concord', V. arizonica 'b42-26', V. rupestris × V. cinerea 'Ill547-1', and Fennell 6 V. aestivalis × Malaga V. vinifera 'DVIT0166') to canker formation by seven trunk pathogens (Neofusicoccum parvum, Lasiodiplodia theobromae, Phaeomoniella chlamydospora, Togninia minima, Phomopsis viticola, Eutypa lata, and an undescribed Eutypa sp.). Susceptibility was based on the length of wood discoloration (LWD) in the woody stems of rooted plants in duplicate greenhouse experiments. Cultivars of V. vinifera and Concord did not vary significantly in susceptibility to N. parvum or L. theobromae (LWD of 21 to 88 mm at 14 weeks post inoculation; P > 0.16), suggesting that they are similarly susceptible to Botryosphaeria dieback. The table-grape Thompson Seedless was most susceptible to P. viticola (mean LWD of 61 mm at 11 months post inoculation; P < 0.0001). V. vinifera cultivars and Concord showed similar susceptibility to the Esca pathogens, Phaeomoniella chlamydospora and T. minima. Susceptibility to E. lata was greatest in V. arizonica b42-26 (mean LWD of 96 mm at 11 months post inoculation; P < 0.03). In fact, all four American Vitis spp. were more susceptible to Eutypa dieback than the V. vinifera cultivars. Our findings suggest that no one cultivar is likely to provide resistance to the range of trunk pathogens but that certain cultivars may be promising candidates for commercially relevant host resistance in grape-production systems where the dominant cultivars are very susceptible.
Esca is a complex grapevine trunk disease associated with fungal infection of the xylem. However, the inconstancy of external symptoms and the ability of esca-associated fungi to inhabit grapevines ...without causing apparent disease suggests that abiotic factors might be involved in the disease. Water stress has been proposed to be one of the factors influencing esca symptom manifestation but the specific role played by water stress on esca development is unknown. We conducted a proton nuclear magnetic resonance spectroscopy-based metabolomic study aiming at unveiling drought-induced modifications in xylem sap composition that could contribute to esca-related infection progression. Vitis vinifera 'Chardonnay' plants were inoculated with Phaeomoniella chlamydospora or Phaeoacremonium minimum and exposed to water stress. Using this approach, 28 metabolites were identified in xylem sap. The results show that water stress induces a concentration increase of most metabolites in xylem sap. An average increase >100% was found for asparagine, isoleucine, leucine, methionine, phenylalanine, proline, tyrosine, valine, sarcosine, and trigonelline. The increase of these compounds seems to be also modulated by fungal infection. This study offers further support to the putative role of drought in esca expression, and opens new avenues of research by extending the current knowledge about metabolites possibly involved in esca disease.
This study investigates the diversity and taxonomy of Cryptosphaeria species occurring in the western United States on the basis of morphological characters and multilocus phylogenetic analyses of ...the ribosomal internal transcribed spacer region, parts of a β-tubulin gene, the DNA-dependent RNA polymerase II second-largest subunit gene and the nuclear ribosomal large subunit gene. Cryptosphaeria multicontinentalis sp. nov is described from the Sierra Nevada and central coast of California on Populus tremuloides, P. balsamifera subsp. trichocarpa and P. fremontii. Cryptosphaeria pullmanensis is reported from a wide geographic area in the western United States on the main host, P. fremontii. The pathogen C. lignyota is reported for the first time from the Sierra Nevada of California on P. tremuloides. The phylogenetic analyses showed that C. multicontinentalis is a sister species to C. lignyota. Both species were closely related to C. subcutanea and more distantly related to C. pullmanensis. Characteristics of both teleomorph and anamorph of the newly introduced species C. multicontinentalis are described and illustrated.
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Let $L$ be a line bundle on a proper, geometrically reduced scheme $X$ over a
non-trivially valued non-Archimedean field $K$. Roughly speaking, the
non-Archimedean volume of a continuous metric on ...the Berkovich analytification
of $L$ measures the asymptotic growth of the space of small sections of tensor
powers of $L$. For a continuous semipositive metric on $L$ in the sense of
Zhang, we show first that the non-Archimedean volume agrees with the energy.
The existence of such a semipositive metric yields that $L$ is nef. A second
result is that the non-Archimedean volume is differentiable at any semipositive
continuous metric. These results are known when $L$ is ample, and the purpose
of this paper is to generalize them to the nef case. The method is based on a
detailed study of the content and the volume of a finitely presented torsion
module over the (possibly non-noetherian) valuation ring of $K$.
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