Publications

Papers on Shimura varieties:

[1] Arithmetic models for Hilbert-Blumenthal modular varieties. Thesis, Columbia University 1992.

[2]  Singularit'es des espaces de modules de Hilbert en caract'eristiques divisant le discriminant. (with P. Deligne), Compositio Mathematica 90 (1994), 59-79.

[3]  Arithmetic models for Hilbert modular varieties. Compositio Mathematica 98 (1995), 43-76.

[18] On the arithmetic moduli schemes of PEL Shimura varieties. Journal of Algebraic Geometry 9 (2000), no. 3, 577-605.

[24]  Local models in the ramified case I. The EL-case. (with M. Rapoport), Journal of Algebraic Geometry, 12 (2003), 107-145.

[26]  Local models in the ramified case II. Splitting models. (with M. Rapoport), Duke Math. J. 127 (2005), no. 2, 193-250.

[34] Local models in the ramified case III. Unitary groups. (with M. Rapoport), J. Inst. Math. Jussieu 8 (2009), no. 3, 507-564.

[38] Local models of Shimura varieties, I. Geometry and combinatorics. (with M. Rapoport, B. Smithling), Handbook of Moduli, vol. III, 135-219. International Press of Boston, Inc., Edited by I. Morrison, G. Farkas. [arXiv:1011.5551]

[39]  Local Models of Shimura varieties and a conjecture of Kottwitz. (with X. Zhu), Inventiones Math. 194, (2013), no. 1, 147–254.  [arXiv:1110.5588]

[40] On the supersingular locus of the ${\rm GU}(2,2)$ Shimura variety. (with B. Howard),   Algebra and Number Theory 8 (2014), no. 7, 1659--1699. [arXiv:1310.4448] 

[46] Rapoport-Zink spaces for spinor groups. (with B. Howard), Compositio Math. 153 (2017), no. 5, 1050--1118.

[48] Integral models of Shimura varieties with parahoric level structure. (with M. Kisin),  Pub. Math. de l' IHES, 128 (2018), 121--218. 

[49] Arithmetic models for Shimura varieties. Proceedings of the ICM in Rio, Brazil 2018.

[51] (G, \mu)-displays and Rapoport-Zink spaces. (with O. Bueltel), J. Inst. Math. Jussieu 19 (2020), no. 4, 1211--1257. 

[53]  Good and semi-stable reductions of Shimura varieties, (with X. He, M.~Rapoport),  Journal de l''Ecole polytechnique -- Math., 7 (2020), 497--571. 

[55] On integral models of Shimura varieties. Math. Annalen. 385 (2023), no. 3-4, 2037–2097. 

[56] Regular integral models for Shimura varieties of orthogonal type (with I. Zachos), Compos. Math. 158 (2022), no. 4, 831–867. arxiv.org/abs/2102.02687 

[57] p-adic shtukas and the theory of global and local Shimura varieties (with M. Rapoport), Cambridge Journal of Math. 12 (2024), no. 1, 1-164.  arxiv.org/abs/2106.08270 

Papers on Galois modules:

[4]  Galois structure of K--groups of rings of integers. (with T. Chinburg, M. Kolster, V. Snaith). Comptes Rendus Acad. Sci. t. 320, S'erie. I,  p. 1435-1440, (1995).

[7] epsilon constants and the Galois structure of de Rham cohomology. (with T. Chinburg, B. Erez, M. Taylor), Annals of Math. 156 (2) (1997), 411-473.

 [8] Quaternionic exercises in K-theory Galois module structure. (with T. Chinburg, M. Kolster, V. Snaith). Algebraic K-theory (Toronto, ON, 1996), 1-29, Fields Inst. Commun., 16, Amer. Math. Soc., Providence, RI, 1997.

[10]  Galois modules and the Theorem of the Cube. Inventiones Math., 133 (1998), 193-225.

[12] Galois structure of K-groups of rings of integers. (with T. Chinburg, M. Kolster, V. Snaith), K-theory 14 (1998), no. 4, 319-369.

[14] Localization of Grothendieck groups and Galois structure. (with T. Chinburg, B. Erez, M. Taylor), Recent progress in Algebra (Taejon/Seoul 1997), 47-63, Contemp. Math. 224. AMS. 1999.

 [15] Nearly perfect complexes and Galois module structure. (with T. Chinburg, M. Kolster, V. Snaith), Compositio Math. 119 (1999), 2, 135-158.

 [16] Epsilon constants and the Galois structure of deRham cohomology II. (with T. Chinburg, M. Taylor), J. Reine Angew. Math. 519 (2000), 201-230.

[17]  Galois module structure and the gamma-filtration. Compositio Math. 121 (2000), no. 1, 79-104.

[21]  On arithmetic class invariants. (with A. Agboola), Math. Annalen 320 (2001) 3, 339-365.

[22] Epsilon constants and equivariant Arakelov Euler characteristics. (with T. Chinburg and M. Taylor), Ann. Sci. 'Ecole Norm. Sup. (4) 35 (2002), 307-352.  

[25]  Duality and Hermitian Galois module structure. (with T. Chinburg and M. Taylor), Proc. London Math. Soc. (3) 87 (2003), no. 1, 54-108.

[28] Pfaffians, the G-signature Theorem and Galois Hodge discriminants. (with T. Chinburg and M. Taylor), Compositio Math., 143, (2007), no. 5, 1213-1254.

[30] Galois structure of unramified covers. Math. Annalen, 341 (2008), 71-97.

[33] Cubic structures, equivariant Euler characteristics and modular forms. (with T. Chinburg and M. Taylor), Annals of Math. (2) 170 (2009) no. 2, 561-608.

[44]  Adams operations and Galois structure. Algebra and Number theory 9 (2015), no. 6, 1477-1514. [arXiv:1309.1661]

[45] Higher adeles and non-abelian Riemann-Roch. (with T. Chinburg, M. Taylor), Advances in Math. 281 (2015), 928-1024 [arXiv:1204.4520]

Other papers:

[5] Tame actions of groups schemes; integrals and slices. (with T. Chinburg, B. Erez, M. Taylor), Duke Math. Journal. 82 (1996), 269-308.

[6]  On the epsilon constants of a variety over a finite field. (with T. Chinburg, B. Erez, M. Taylor), American Jour. of Math. 119 (1997), 503-522.

[9]  Riemann-Roch theorems for arithmetic schemes with a group action. (with T. Chinburg, B. Erez, M. Taylor), J. Reine Angew. Math. 189 (1997), 151-187.

[11]  On torsion line bundles and torsion points on abelian varieties. Duke Math. Journal. 91 (1998), 215--224.

[13] On the epsilon constants of arithmetic schemes. (with T. Chinburg, B. Erez, M. Taylor), Math Annalen 311 (1998) 2, 377-395.

[19]  Epsilon constants and Arakelov Euler characteristics. (with T. Chinburg, M. Taylor), Math. Research Letters, vol. 7, no. 4 (2000), 433-447.

[20]  Line bundles, rational points and ideal classes.(with A. Agboola), Math. Research Letters, vol. 7, no. 5-6 (2000), 709-718.

[23]  Discriminants and Arakelov Euler characteristics. (with T. Chinburg and M. Taylor), Number Theory for the Millennium (Proc. Millennial Conf. Number Theory, May 21-26, 2000, Urbana, IL, M. Bennett et al., eds.), Vol. I, A. K. Peters, Wellesley, MA, 2002, 229-255.

[27] Cubic structures and ideal class groups. Ann. Sci. 'Ecole Norm. Sup. (4) 38 (2005), no. 3, 471-503.

[29] Integral Grothendieck-Riemann-Roch theorem. Inventiones Math., 170 (2007), 455-481.

[31] Grothendieck-Riemann-Roch and the moduli of Enriques surfaces. Mathematical Research Letters. 15 (2008), no. 1, 117-120.

[32] Twisted loop groups and their affine flag varieties. (with M. Rapoport), Advances in Math. 219 (2008), no. 1, 118--198.

[35] Some questions about G-bundles over curves. (with M. Rapoport), Algebraic and arithmetic structures of moduli spaces (Sapporo 2007), Adv. Stud. Pure Math., 58, Math. Soc. Japan, Tokyo, 2010, 159-171.

[36]  Phi-modules and coefficient spaces. (with M. Rapoport), Moscow Math. Journal, Vol. 9 (2009), no. 3, (issue dedicated to P. Deligne), 625-663.

[37] K_1 of a p-adic group ring I. The determinantal image. (with T. Chinburg, M. Taylor), Journal of Algebra, v. 326, Issue 1, 15 (2011), 74-112.

[41] The group logarithm past and present. (with T. Chinburg, M. Taylor), in ``Noncommutative Iwasawa Main Conjectures over Totally Real Fields" Springer Proceedings in Mathematics & Statistics Volume 29, 2013, pp 51-78 [pdf]

[42] K_1 of a p-adic group ring II. The determinantal kernel SK_1. (with T. Chinburg,  M. Taylor), J. Pure Appl. Algebra 219 (2015), no. 7, 2581--2623. [arxiv:1303:.5337]

[43] Finite morphisms to projective space and capacity theory. (with T. Chinburg, L. Moret-Bailly, M. Taylor),   J. Reine Angew. Math. (Crelle).  727 (2017), 69--84.  [arXiv:1201.0678] 

[47]  Abelian Arithmetic Chern-Simons Theory and Arithmetic Linking Numbers. (with   H.-J. Chung, D. Kim,  M. Kim,  J. Park, H. Yoo), International Mathematics Research Notices (IMRN) 2019, no. 18, 5674--5702. 

 Erratum:  Int. Math. Res. Not. IMRN 2019, no. 18, 5854--5857. 

[50] Cup products in the 'etale cohomology of number fields. (with F. Bleher, T. Chinburg,   R.~Greenberg, M.~Kakde, M. Taylor), New York J. Math. 24 (2018) 513-541.

[52]  Higher Chern classes in Iwasawa Theory. (with F. Bleher, T. Chinburg, R. Greenberg, M.~Kakde, R.~Sharifi, M. Taylor), American Journal of Math., 142 (2020), no. 2, 627--682. 

[54]  Volume and symplectic structure for $\ell$-adic local systems. Advances in Math. 387 (2021), Paper No. 107836, 70 pp. arxiv.org/abs/2006.03668