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Journal articles on the topic 'Shimura varietie'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

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

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2

Giacomini, Michele. "Holomorphic curves in Shimura varieties." Archiv der Mathematik 111, no. 4 (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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3

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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4

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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5

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

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6

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

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7

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

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8

Fargues, Laurent, Ulrich Görtz, Eva Viehmann, and Torsten Wedhorn. "Arithmetic of Shimura Varieties." Oberwolfach Reports 20, no. 1 (2023): 261–326. http://dx.doi.org/10.4171/owr/2023/5.

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9

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 (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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10

Boyer, Pascal. "Conjecture de monodromie-poids pour quelques variétés de Shimura unitaires." Compositio Mathematica 146, no. 2 (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 Shi

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11

Shin, Sug Woo. "A stable trace formula for Igusa varieties." Journal of the Institute of Mathematics of Jussieu 9, no. 4 (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 ou

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12

Pappas, G., and M. Rapoport. "Local models in the ramified case. III Unitary groups." Journal of the Institute of Mathematics of Jussieu 8, no. 3 (2009): 507–64. http://dx.doi.org/10.1017/s1474748009000139.

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AbstractWe continue our study of the reduction of PEL Shimura varieties with parahoric level structure at primespat which the group defining the Shimura variety ramifies. We describe ‘good’p-adic integral models of these Shimura varieties and study their étale local structure. In the present paper we mainly concentrate on the case of unitary groups for a ramified quadratic extension. Some of our results are applications of the theory of twisted affine flag varieties that we developed in a previous paper.

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13

Blasius, Don, and Lucio Guerberoff. "Complex conjugation and Shimura varieties." Algebra & Number Theory 11, no. 10 (2017): 2289–321. http://dx.doi.org/10.2140/ant.2017.11.2289.

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14

Mok, Pila, and Tsimerman. "Ax-Schanuel for Shimura varieties." Annals of Mathematics 189, no. 3 (2019): 945. http://dx.doi.org/10.4007/annals.2019.189.3.7.

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15

Harris, Michael, and Steven Zucker. "Boundary cohomology of Shimura varieties." Inventiones Mathematicae 116, no. 1 (1994): 243–308. http://dx.doi.org/10.1007/bf01231562.

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16

Hida, Haruzo. "Automorphism groups of Shimura varieties." Documenta Mathematica 11 (2006): 25–56. http://dx.doi.org/10.4171/dm/203.

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17

Ullmo, Emmanuel, and Andrei Yafaev. "Algebraic flows on Shimura varieties." manuscripta mathematica 155, no. 3-4 (2017): 355–67. http://dx.doi.org/10.1007/s00229-017-0949-0.

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18

Tian, Yichao, and Liang Xiao. "On Goren–Oort stratification for quaternionic Shimura varieties." Compositio Mathematica 152, no. 10 (2016): 2134–220. http://dx.doi.org/10.1112/s0010437x16007326.

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Let $F$ be a totally real field in which a prime $p$ is unramified. We define the Goren–Oort stratification of the characteristic-$p$ fiber of a quaternionic Shimura variety of maximal level at $p$. We show that each stratum is a $(\mathbb{P}^{1})^{r}$-bundle over other quaternionic Shimura varieties (for an appropriate integer $r$). As an application, we give a necessary condition for the ampleness of a modular line bundle on a quaternionic Shimura variety in characteristic $p$.

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19

van Hoften, Pol, and Luciena Xiao Xiao. "Monodromy and Irreducibility of Igusa Varieties." American Journal of Mathematics 147, no. 2 (2025): 355–400. https://doi.org/10.1353/ajm.2025.a954646.

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abstract: We determine the irreducible components of Igusa varieties for Shimura varieties of Hodge type under a mild condition and use that to compute the irreducible components of central leaves. In particular, we show that a strong version of the discrete Hecke orbit conjecture is false in general. Our method combines recent work of D'Addezio on monodromy groups of compatible local systems with a generalisation of a method of Hida, using the Honda--Tate theory for Shimura varieties of Hodge type developed by Kisin--Madapusi Pera--Shin. We also determine the irreducible components of Newton

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20

Andreatta, Fabrizio, Eyal Z. Goren, Benjamin Howard, and Keerthi Madapusi Pera. "Height pairings on orthogonal Shimura varieties." Compositio Mathematica 153, no. 3 (2017): 474–534. http://dx.doi.org/10.1112/s0010437x1600779x.

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Let $M$ be the Shimura variety associated to the group of spinor similitudes of a quadratic space over $\mathbb{Q}$ of signature $(n,2)$. We prove a conjecture of Bruinier and Yang, relating the arithmetic intersection multiplicities of special divisors and complex multiplication points on $M$ to the central derivatives of certain $L$-functions. Each such $L$-function is the Rankin–Selberg convolution associated with a cusp form of half-integral weight $n/2+1$, and the weight $n/2$ theta series of a positive definite quadratic space of rank $n$. When $n=1$ the Shimura variety $M$ is a classica

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21

Virdol, Cristian. "On L-Functions of Twisted 3-Dimensional Quaternionic Shimura Varieties." Nagoya Mathematical Journal 190 (2008): 87–104. http://dx.doi.org/10.1017/s0027763000009570.

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In this paper we compute and continue meromorphically to the entire complex plane the zeta functions of twisted quaternionic Shimura varieties of dimension 3. The twist of the quaternionic Shimura varieties is done by a mod ℘ representation of the absolute Galois group.

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22

Madapusi Pera, Keerthi. "Integral canonical models for Spin Shimura varieties." Compositio Mathematica 152, no. 4 (2015): 769–824. http://dx.doi.org/10.1112/s0010437x1500740x.

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We construct regular integral canonical models for Shimura varieties attached to Spin and orthogonal groups at (possibly ramified) primes$p>2$where the level is not divisible by$p$. We exhibit these models as schemes of ‘relative PEL type’ over integral canonical models of larger Spin Shimura varieties with good reduction at$p$. Work of Vasiu–Zink then shows that the classical Kuga–Satake construction extends over the integral models and that the integral models we construct are canonical in a very precise sense. Our results have applications to the Tate conjecture for K3 surfaces, as well

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23

Shen, Xu. "ON THE -ADIC COHOMOLOGY OF SOME -ADICALLY UNIFORMIZED SHIMURA VARIETIES." Journal of the Institute of Mathematics of Jussieu 17, no. 5 (2016): 1197–226. http://dx.doi.org/10.1017/s1474748016000360.

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We determine the Galois representations inside the$\ell$-adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinfeld upper half spaces. Our main results confirm Langlands–Kottwitz’s description of the cohomology of Shimura varieties in new cases.

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24

Sankaran, Siddarth. "Unitary cycles on Shimura curves and the Shimura lift II." Compositio Mathematica 150, no. 12 (2014): 1963–2002. http://dx.doi.org/10.1112/s0010437x14007507.

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AbstractWe consider two families of arithmetic divisors defined on integral models of Shimura curves. The first was studied by Kudla, Rapoport and Yang, who proved that if one assembles these divisors in a formal generating series, one obtains the$q$-expansion of a modular form of weight 3/2. The present work concerns the Shimura lift of this modular form: we identify the Shimura lift with a generating series comprising divisors arising in the recent work of Kudla and Rapoport regarding cycles on Shimura varieties of unitary type. In the prequel to this paper, the author considered the geometr

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25

Rapoport, M., B. Smithling, and W. Zhang. "Arithmetic diagonal cycles on unitary Shimura varieties." Compositio Mathematica 156, no. 9 (2020): 1745–824. http://dx.doi.org/10.1112/s0010437x20007289.

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We define variants of PEL type of the Shimura varieties that appear in the context of the arithmetic Gan–Gross–Prasad (AGGP) conjecture. We formulate for them a version of the AGGP conjecture. We also construct (global and semi-global) integral models of these Shimura varieties and formulate for them conjectures on arithmetic intersection numbers. We prove some of these conjectures in low dimension.

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26

Chen, Ke, Xin Lu, and Kang Zuo. "On the Oort conjecture for Shimura varieties of unitary and orthogonal types." Compositio Mathematica 152, no. 5 (2016): 889–917. http://dx.doi.org/10.1112/s0010437x15007794.

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In this paper we study the Oort conjecture concerning the non-existence of Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety${\mathcal{A}}_{g}$. Using the poly-stability of Higgs bundles on curves and the slope inequality of Xiao on fibered surfaces, we show that a Shimura curve$C$is not contained generically in the Torelli locus if its canonical Higgs bundle contains a unitary Higgs subbundle of rank at least$(4g+2)/5$. From this we prove that a Shimura subvariety of$\mathbf{SU}(n,1)$type is not contained generically in the Torelli locus when a nume

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27

Cadoret, Anna, and Arno Kret. "Galois-generic points on Shimura varieties." Algebra & Number Theory 10, no. 9 (2016): 1893–934. http://dx.doi.org/10.2140/ant.2016.10.1893.

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28

de Shalit, Ehud, and Eyal Z. Goren. "Theta operators on unitary Shimura varieties." Algebra & Number Theory 13, no. 8 (2019): 1829–77. http://dx.doi.org/10.2140/ant.2019.13.1829.

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29

Rapoport, M., B. Smithling, and W. Zhang. "On Shimura varieties for unitary groups." Pure and Applied Mathematics Quarterly 17, no. 2 (2021): 773–837. http://dx.doi.org/10.4310/pamq.2021.v17.n2.a8.

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30

Kisin, Mark. "Integral canonical models of Shimura varieties." Journal de Théorie des Nombres de Bordeaux 21, no. 2 (2009): 301–12. http://dx.doi.org/10.5802/jtnb.672.

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31

James S. Milne and Junecue Suh. "Nonhomeomorphic conjugates of connected Shimura varieties." American Journal of Mathematics 132, no. 3 (2010): 731–50. http://dx.doi.org/10.1353/ajm.0.0112.

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32

Rotger, Victor. "Modular Shimura varieties and forgetful maps." Transactions of the American Mathematical Society 356, no. 4 (2003): 1535–50. http://dx.doi.org/10.1090/s0002-9947-03-03408-1.

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33

Görtz, Ulrich, Xuhua He, and Sian Nie. "Fully Hodge–Newton Decomposable Shimura Varieties." Peking Mathematical Journal 2, no. 2 (2019): 99–154. http://dx.doi.org/10.1007/s42543-019-00013-2.

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34

Ullmo, Emmanuel, and Andrei Yafaev. "Holomorphic curves in compact Shimura varieties." Annales de l’institut Fourier 68, no. 2 (2018): 647–59. http://dx.doi.org/10.5802/aif.3174.

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35

Haines, Thomas J. "On Connected Components of Shimura Varieties." Canadian Journal of Mathematics 54, no. 2 (2002): 352–95. http://dx.doi.org/10.4153/cjm-2002-012-x.

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AbstractWe study the cohomology of connected components of Shimura varieties coming from the group GSp2g, by an approach modeled on the stabilization of the twisted trace formula, due to Kottwitz and Shelstad. More precisely, for each character ϖ on the group of connected components of we define an operator L(ω) on the cohomology groups with compact supports Hic(, ), and then we prove that the virtual trace of the composition of L(ω) with a Hecke operator f away from p and a sufficiently high power of a geometric Frobenius , can be expressed as a sum of ω-weighted (twisted) orbital integrals (

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36

Gärtner, Jérôme. "Darmon’s Points and Quaternionic Shimura Varieties." Canadian Journal of Mathematics 64, no. 6 (2012): 1248–88. http://dx.doi.org/10.4153/cjm-2011-086-5.

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Abstract In this paper, we generalize a conjecture due to Darmon and Logan in an adelic setting. We study the relation between our construction and Kudla's works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a Gross-Kohnen-Zagier theorem for Darmon's points.

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37

Harris, Michael, and Richard Taylor. "Regular models of certain Shimura varieties." Asian Journal of Mathematics 6, no. 1 (2002): 61–94. http://dx.doi.org/10.4310/ajm.2002.v6.n1.a4.

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38

Richard, Rodolphe, and Andrei Yafaev. "Generalised André–Pink–Zannier conjecture for Shimura varieties of abelian type." Comptes Rendus. Mathématique 363, G9 (2025): 873–78. https://doi.org/10.5802/crmath.751.

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This note describes the results of [6]. The main result is the proof of the Generalised André–Pink–Zannier conjecture in Shimura varieties of abelian type. The core result is a lower bound, in terms of height functions defined in [7], for the sizes of Galois orbits of points in generalised Hecke orbits, which is unconditional for Shimura varieties of abelian type.

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39

Jan Nekovar. "Eichler-Shimura relations and semisimplicity of étale cohomology of quaternionic Shimura varieties." Annales scientifiques de l'École normale supérieure 51, no. 5 (2018): 1179–252. http://dx.doi.org/10.24033/asens.2374.

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40

Linowitz, Benjamin, and Matthew Stover. "Parametrizing Shimura subvarieties of $${\mathrm{A}_1}$$ Shimura varieties and related geometric problems." Archiv der Mathematik 107, no. 3 (2016): 213–26. http://dx.doi.org/10.1007/s00013-016-0944-9.

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41

Lee, Min. "Mixed automorphic vector bundles on Shimura varieties." Pacific Journal of Mathematics 173, no. 1 (1996): 105–26. http://dx.doi.org/10.2140/pjm.1996.173.105.

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42

Caraiani, Ana, Daniel R. Gulotta, Chi-Yun Hsu, et al. "Shimura varieties at level and Galois representations." Compositio Mathematica 156, no. 6 (2020): 1152–230. http://dx.doi.org/10.1112/s0010437x20007149.

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We show that the compactly supported cohomology of certain $\text{U}(n,n)$- or $\text{Sp}(2n)$-Shimura varieties with $\unicode[STIX]{x1D6E4}_{1}(p^{\infty })$-level vanishes above the middle degree. The only assumption is that we work over a CM field $F$ in which the prime $p$ splits completely. We also give an application to Galois representations for torsion in the cohomology of the locally symmetric spaces for $\text{GL}_{n}/F$. More precisely, we use the vanishing result for Shimura varieties to eliminate the nilpotent ideal in the construction of these Galois representations. This streng

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43

Varshavsky, Yakov. "p-adic uniformization of unitary Shimura varieties." Publications mathématiques de l'IHÉS 87, no. 1 (1998): 57–119. http://dx.doi.org/10.1007/bf02698861.

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44

Varshavsky, Y. "On the characterization of complex Shimura varieties." Selecta Mathematica 8, no. 2 (2002): 283–314. http://dx.doi.org/10.1007/s00029-002-8107-1.

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45

Milne, J. S. "Automorphic vector bundles on connected Shimura varieties." Inventiones Mathematicae 92, no. 1 (1988): 91–128. http://dx.doi.org/10.1007/bf01393994.

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46

Vasiu, Adrian. "Integral Canonical Models of Unitary Shimura Varieties." Asian Journal of Mathematics 12, no. 2 (2008): 151–76. http://dx.doi.org/10.4310/ajm.2008.v12.n2.a1.

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47

Imai, Naoki, and Yoichi Mieda. "Potentially good reduction loci of Shimura varieties." Tunisian Journal of Mathematics 2, no. 2 (2020): 399–454. http://dx.doi.org/10.2140/tunis.2020.2.399.

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48

Giacomini, Michele. "Correction to: Holomorphic curves in Shimura varieties." Archiv der Mathematik 114, no. 1 (2019): 119–21. http://dx.doi.org/10.1007/s00013-019-01400-y.

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49

He, X., and M. Rapoport. "Stratifications in the reduction of Shimura varieties." manuscripta mathematica 152, no. 3-4 (2016): 317–43. http://dx.doi.org/10.1007/s00229-016-0863-x.

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50

Reimann, Harry. "Reduction of Shimura varieties at parahoric levels." manuscripta mathematica 107, no. 3 (2002): 355–90. http://dx.doi.org/10.1007/s002290200244.

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