Relevant bibliographies by topics / Algebraic varieties. Hilbert modular surfaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Algebraic varieties. Hilbert modular surfaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Algebraic varieties. Hilbert modular surfaces"

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Goldring, Wushi, and Jean-Stefan Koskivirta. "Automorphic vector bundles with global sections on -schemes." Compositio Mathematica 154, no. 12 (2018): 2586–605. http://dx.doi.org/10.1112/s0010437x18007467.

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A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of $G$-zips of connected Hodge type; such schemes should include all Hodge-type Shimura varieties with hyperspecial level. We prove our conjecture for groups of type $A_{1}^{n}$, $C_{2}$, and $\mathbf{F}_{p}$-split groups of type $A_{2}$ (this includes all Hilbert–Blumenthal varieties and should also apply to Siegel modular $3$-folds and Picard modular surfaces). An example is given to show that our conjecture can fail for z
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Howard, Benjamin. "Intersection theory on Shimura surfaces." Compositio Mathematica 145, no. 2 (2009): 423–75. http://dx.doi.org/10.1112/s0010437x09003935.

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AbstractKudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, in which one intersects two codimension one cycles on the integral model of a Shimura curve, has been completed by Kudla, Rapoport and Yang. In the present paper we prove results in a higher dimensional setting. On the integral model of a Shimura surface we consider the intersection of a Shimura curve with a codimension two cycle of complex multiplication points, and relate the intersectio
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Suh, Junecue. "Ordinary primes in Hilbert modular varieties." Compositio Mathematica 156, no. 4 (2020): 647–78. http://dx.doi.org/10.1112/s0010437x19007826.

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A well-known conjecture, often attributed to Serre, asserts that any motive over any number field has infinitely many ordinary reductions (in the sense that the Newton polygon coincides with the Hodge polygon). In the case of Hilbert modular cuspforms $f$ of parallel weight $(2,\ldots ,2)$, we show how to produce more ordinary primes by using the Sato–Tate equidistribution and combining it with the Galois theory of the Hecke field. Under the assumption of stronger forms of Sato–Tate equidistribution, we get stronger (but conditional) results. In the case of higher weights, we formulate the ord
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GETZ, JAYCE R., and HEEKYOUNG HAHN. "ALGEBRAIC CYCLES AND TATE CLASSES ON HILBERT MODULAR VARIETIES." International Journal of Number Theory 10, no. 01 (2014): 161–76. http://dx.doi.org/10.1142/s1793042113500875.

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Let E/ℚ be a totally real number field that is Galois over ℚ, and let π be a cuspidal, nondihedral automorphic representation of GL 2(𝔸E) that is in the lowest weight discrete series at every real place of E. The representation π cuts out a "motive" M ét (π∞) from the ℓ-adic middle degree intersection cohomology of an appropriate Hilbert modular variety. If ℓ is sufficiently large in a sense that depends on π we compute the dimension of the space of Tate classes in M ét (π∞). Moreover if the space of Tate classes on this motive over all finite abelian extensions k/E is at most of rank one as a
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Dimitrov, Mladen. "On Ihara’s lemma for Hilbert modular varieties." Compositio Mathematica 145, no. 5 (2009): 1114–46. http://dx.doi.org/10.1112/s0010437x09004205.

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AbstractLet ρ be a two-dimensional modulo p representation of the absolute Galois group of a totally real number field. Under the assumptions that ρ has a large image and admits a low-weight crystalline modular deformation we show that any low-weight crystalline deformation of ρ unramified outside a finite set of primes will be modular. We follow the approach of Wiles as generalized by Fujiwara. The main new ingredient is an Ihara-type lemma for the local component at ρ of the middle degree cohomology of a Hilbert modular variety. As an application we relate the algebraic p-part of the value a
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McREYNOLDS, D. B. "Cusps of Hilbert modular varieties." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (2008): 749–59. http://dx.doi.org/10.1017/s0305004107001004.

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AbstractMotivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifoldMto be diffeomorphic to a cusp cross-section of a Hilbert modular variety. Specialized to Hilbert modular surfaces, this proves that every Sol 3–manifold is diffeo morphic to a cusp cross-section of a (generalized) Hilbert modular surface. We also deduce an obstruction to geometric bounding in this setting. Consequently, there exist Sol 3–manifolds that cannot arise as a cusp cross-section of a 1–cusped n
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Virdol, Cristian. "Algebraic cycles on a product of two Hilbert modular surfaces." Transactions of the American Mathematical Society 362, no. 07 (2010): 3691–703. http://dx.doi.org/10.1090/s0002-9947-10-05116-0.

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Kumar, Abhinav, and Ronen E. Mukamel. "Real multiplication through explicit correspondences." LMS Journal of Computation and Mathematics 19, A (2016): 29–42. http://dx.doi.org/10.1112/s1461157016000188.

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We compute equations for real multiplication on the divisor classes of genus-2 curves via algebraic correspondences. We do so by implementing van Wamelen’s method for computing equations for endomorphisms of Jacobians on examples drawn from the algebraic models for Hilbert modular surfaces computed by Elkies and Kumar. We also compute a correspondence over the universal family for the Hilbert modular surface of discriminant $5$ and use our equations to prove a conjecture of A. Wright on dynamics over the moduli space of Riemann surfaces.
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Yang, Tonghai. "The Chowla–Selberg Formula and The Colmez Conjecture." Canadian Journal of Mathematics 62, no. 2 (2010): 456–72. http://dx.doi.org/10.4153/cjm-2010-028-x.

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AbstractIn this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.
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Berman, Robert J., and Gerard Freixas i Montplet. "An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms." Compositio Mathematica 150, no. 10 (2014): 1703–28. http://dx.doi.org/10.1112/s0010437x14007325.

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AbstractWe prove arithmetic Hilbert–Samuel type theorems for semi-positive singular hermitian line bundles of finite height. This includes the log-singular metrics of Burgos–Kramer–Kühn. The results apply in particular to line bundles of modular forms on some non-compact Shimura varieties. As an example, we treat the case of Hilbert modular surfaces, establishing an arithmetic analogue of the classical result expressing the dimensions of spaces of cusp forms in terms of special values of Dedekind zeta functions.
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Dissertations / Theses on the topic "Algebraic varieties. Hilbert modular surfaces"

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Koehl, Jürgen. "Algebraische Zykel auf Hilbertschen Modulflächen." Bonn : Reinische Friedrich-Wilhelms-Universität, 1987. http://catalog.hathitrust.org/api/volumes/oclc/17561108.html.

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Liu, Sheng-Chi. "Mass equidistribution of Hecke eigenforms on the Hilbert modular varieties." Columbus, Ohio : Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1242747349.

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Tari, Kévin. "Automorphismes des variétés de Kummer généralisées." Thesis, Poitiers, 2015. http://www.theses.fr/2015POIT2301/document.

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Dans ce travail, nous classifions les automorphismes non-symplectiques des variétés équivalentes par déformations à des variétés de Kummer généralisées de dimension 4, ayant une action d'ordre premier sur le réseau de Beauville-Bogomolov. Dans un premier temps, nous donnons les lieux fixes des automorphismes naturels de cette forme. Par la suite, nous développons des outils sur les réseaux en vue de les appliquer à nos variétés. Une étude réticulaire des tores complexes de dimension 2 permet de mieux comprendre les automorphismes naturels sur les variétés de type Kummer. Nous classifions final
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Books on the topic "Algebraic varieties. Hilbert modular surfaces"

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Alberto, Corso, and Polini Claudia 1966-, eds. Commutative algebra and its connections to geometry: Pan-American Advanced Studies Institute, August 3--14, 2009, Universidade Federal de Pernambuco, Olinda, Brazil. American Mathematical Society, 2011.

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Hilbert modular forms and Iwasawa theory. Clarendon, 2006.

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Weiß, Christian. Twisted Teichmüller Curves. Springer, 2014.

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Hilbert Modular Forms: Mod P And P-adic Aspects (Memoirs of the American Mathematical Society). American Mathematical Society, 2005.

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Book chapters on the topic "Algebraic varieties. Hilbert modular surfaces"

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Edixhoven, Bas. "On the André-Oort Conjecture for Hilbert Modular Surfaces." In Moduli of Abelian Varieties. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0_4.

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Van de Ven, A. "Hilbert modular surfaces and the classification of algebraic surfaces." In Gesammelte Abhandlungen/Collected Papers. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-61711-9_19.

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Hirzebruch, Friedrich. "The Hilbert modular group and some algebraic surfaces." In Gesammelte Abhandlungen/Collected Papers. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-61711-9_16.

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