Research Interests

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

Selected Publications of 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 Publications

$\bullet $ U. Hartl and W. Kim. Local Shtukas, Hodge-Pink Structures and Galois Representations, pages 157–218. European Mathematical Society (EMS), Zürich, January 2020. arXiv:1512.05893.

$\bullet $ U. Hartl and A.-K. Juschka. Pink's theory of Hodge structures and the Hodge conjecture over function fields, pages 35–155. European Mathematical Society (EMS), Zürich, January 2020. arXiv:1607.01412.

$\bullet $ E. Arasteh Rad and U. Hartl. Uniformizing the Moduli Stacks of Global G-Shtukas. International Mathematics Research Notices, November 2019. doi:10.1093/imrn/rnz223.

$\bullet $ U. Hartl and R. K. Singh. Local shtukas and divisible local Anderson modules. Canadian Journal of Mathematics, 71(5):1163–1207, March 2019. doi:10.4153/cjm-2018-016-2.

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

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

$\bullet $ U. Hartl and E. Viehmann. The generic fiber of moduli spaces of bounded local $G$-shtukas. arXiv e-prints, December 2017. URL:, arXiv:1712.07936.