Topics in Mathematics Münster

Research Interests

$\bullet$ Arithmetic algebraic geometry.
$\bullet$ Algebraic number theory.
$\bullet$ Arithmetic of function fields.
$\bullet$ Structure theory of Shimura varieties and their function field analogues.
$\bullet$ $p$-adic Hodge theory.
$\bullet$ $p$-adic Langlands programme.
$\bullet$ Model theory.

Selected Publications of Prof. Dr. Urs Hartl

$\bullet$ U. Hartl and R. K. Singh. Periods of Drinfeld modules and local shtukas with complex multiplication. J. Inst. Math. Jussieu, 1–34, 2018.

$\bullet$ E. Arasteh Rad and U. Hartl. Local $\mathbb P$-shtukas and their relation to global $\mathfrak G$-shtukas. Münster J. Math., 7(2):623–670, 2014.

$\bullet$ U. Hartl. On a conjecture of Rapoport and Zink. Invent. Math., 193(3):627–696, 2013.

$\bullet$ U. Hartl and E. Viehmann. Foliations in deformation spaces of local $G$-shtukas. Adv. Math., 229(1):54–78, 2012.

$\bullet$ U. Hartl and E. Viehmann. The Newton stratification on deformations of local $G$-shtukas. J. Reine Angew. Math., 656:87–129, 2011.

$\bullet$ U. Hartl. Period spaces for Hodge structures in equal characteristic. Ann. of Math. (2), 173(3):1241–1358, 2011.

$\bullet$ U. Hartl. A dictionary between Fontaine-theory and its analogue in equal characteristic. J. Number Theory, 129(7):1734–1757, 2009.

$\bullet$ U. Hartl. Uniformizing the stacks of abelian sheaves. In Number fields and function fields–two parallel worlds, volume 239 of Progr. Math., pages 167–222. Birkhäuser, Boston, 2005.

$\bullet$ U. Hartl and R. Pink. Vector bundles with a Frobenius structure on the punctured unit disc. Compos. Math., 140(3):689–716, 2004.

$\bullet$ U. Hartl and W. Lütkebohmert. On rigid-analytic Picard varieties. J. Reine Angew. Math., 528:101–148, 2000.

Current Cluster Publications of Prof. Dr. Urs Hartl

$\bullet $ Christoph Böhm and Urs Hartl. Moment map flow on real reductive Lie groups and GIT estimates. arXiv e-prints, June 2024. arXiv:2406.19340.

$\bullet $ Urs Hartl and Yujie Xu. Uniformizing the moduli stacks of global $G$-shtukas II. arXiv e-prints, September 2023. arXiv:2309.17441.

$\bullet $ Urs Hartl and Rajneesh Kumar Singh. Periods of Drinfeld modules and local Shtukas with complex multiplication -– erratum. Journal of the Institute of Mathematics of Jussieu, 21(6):2247–2251, November 2022. doi:10.1017/S1474748020000705.

$\bullet $ Esmail Arasteh Rad and Urs Hartl. Category of $C$-motives over finite fields. J. Number Theory, 232:283–316, July 2022. doi:10.1016/j.jnt.2020.06.015.

$\bullet $ Urs Hartl and Rajneesh Kumar Singh. A short review on local shtukas and divisible local Anderson modules. In Perfectoid Spaces, Infosys Science Foundation Series, pages 51–68. April 2022. doi:10.1007/978-981-16-7121-0_4.

$\bullet $ Esmail Arasteh Rad and Urs Hartl. Uniformizing the moduli stacks of global G-shtukas. International Mathematics Research Notices, pages 16121–16192, November 2021. doi:10.1093/imrn/rnz223.

$\bullet $ Urs Hartl and Eva Viehmann. The generic fibre of moduli spaces of bounded local $G$-shtukas. Journal of the Institute of Mathematics of Jussieu, 22(2):799–878, July 2021. doi:10.1017/s1474748021000293.

$\bullet $ Urs Hartl and Rajneesh Kumar Singh. Product formulas for periods of CM abelian varieties and the function field analog. J. Number Theory, 218:62–151, January 2021. doi:10.1016/j.jnt.2020.06.017.

$\bullet $ Urs Hartl and Chia-Fu Yu. Arithmetic Satake compactifications and algebraic Drinfeld modular forms. arXiv e-prints, September 2020. arXiv:2009.13934.

$\bullet $ Urs Hartl and Eugen Hellmann. The universal family of semistable $p$-adic Galois representations. Algebra Number Theory, 14(5):1055–1121, July 2020. doi:10.2140/ant.2020.14.1055.

$\bullet $ Urs Hartl and Wansu Kim. Local Shtukas, Hodge-Pink Structures and Galois Representations, pages 157–218. EMS Ser. Congr. Rep. EMS Publ. House, Berlin, May 2020. doi:10.4171/198.

$\bullet $ Urs Hartl and Ann-Kristin Juschka. Pink's theory of Hodge structures and the Hodge conjecture over function fields. In $t$-motives: Hodge structures, transcendence and other motivic aspects, pages 31–182. May 2020. doi:10.4171/198-1/2.

$\bullet $ Urs Hartl and Rajneesh Kumar Singh. Periods of Drinfeld modules and local shtukas with complex multiplication. J. Inst. Math. Jussieu, 19(1):175–208, January 2020. doi:10.1017/s1474748017000494.

$\bullet $ Urs Hartl. Isogenies of abelian Anderson A-modules and A-motives. ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 19(4):1429–1470, December 2019. doi:10.2422/2036-2145.201612_003.

$\bullet $ Urs Hartl and Rajneesh Kumar Singh. Local shtukas and divisible local Anderson modules. Canadian J. Math., 71(5):1163–1207, March 2019. doi:10.4153/cjm-2018-016-2.

$\bullet $ Urs Hartl and Ambrus Pál. Crystalline Chebotarëv density theorems. arXiv e-prints, November 2018. arXiv:1811.07084.