Related papers: Shimura varieties and gerbes
In this paper we prove the equidistribution of bounded sequences of special subvarieties in a general mixed Shimura varieties, a notion adapted from the pure case treated by Clozel, Ullmo, and Yafaev in the study of the Andre-Oort…
This note gives simpler proofs of the variational and multiple priors representations in Maccheroni et al. (2006) and Gilboa and Schmeidler (1989).
Igusa varieties are algebraic varieties that arise in the study of special fibers of Shimura varieties, and have demonstrated many applications in the Langlands program via a Langlands-Kottwitz style point-counting formula due to Shin in…
For a much better-founded theory, check Wing Ip, GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L16203, doi:10.1029/2005GL025386, 2006 (see also http://www.agu.org/journals/gl/gl0616/2005GL025386/)
Final version, appeared in C.R. Acad. Sci. Paris 339 (2004), no4, 257--259.
For any Shimura variety of Hodge type with hyperspecial level at a prime $p$ and a lisse sheaf on it, we prove a formula, conjectured by Kottwitz \cite{Kottwitz90}, for the Lefschetz number of an arbitrary Frobenius-twisted Hecke…
This paper is a continuation of our paper math.AG/0006222. We study the reduction of certain PEL Shimura varieties with parahoric level structure at primes p at which the group that defines the Shimura variety ramifies. We describe "good"…
This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.
For an odd prime p, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G,X) of abelian type, such that G splits over a tamely ramified extension of Q_p. The local structure of…
We verify that the descent maps provided by Langlands's Conjugacy Conjecture do satisfy the continuity condition necessary for them to be effective. Thus Langlands's conjecture does imply the existence of canonical models. This replaces an…
Some remarks on the jump condition appearing in Theorems 1.1 and 1.2 in the article [1] and their implications are given.
We deal with some questions posted by Matsumura and Watanabe about the Rees and Dilworth number, and their higher-dimensional versions.
In this paper we prove the equidistribution of certain families of special subvarieties in Kuga varieties, which is a special case of the general Andre-Oort conjecture formulated for mixed Shimura varieties proposed by R.Pink. Our approach…
We make remarks on Ristroph and Zhang's [{\it Phys. Rev. Lett.} 101, 194502 (2008)] paper.
We prove the existence of weak integral canonical models of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic $(0,p)$. As a first application we solve a conjecture of Langlands for Shimura varieties of Hodge type.…
We survey some recent work on the geometric Satake of p-adic groups and its applications to some arithmetic problems of Shimura varieties. We reformulate a few constructions appeared in the previous works more conceptually.
This is an update on, and expansion of, our paper Open problems on $\beta\omega$ in the book Open Problems in Topology.
This is about the paper by Thawhat Changphas and Nawamin Phaipong in Quasigroups and Related Systems 22 (2014), 193--200.
Let $Z$ be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special subvariety of $Z$.
We discuss the relationships between the Andr\'e-Oort, Andr\'e-Pink-Zannier, and Mordell-Lang conjectures for Shimura varieties. We then combine the latter with the geometric Zilber-Pink conjecture to obtain some new results on unlikely…