Some of Mark's Papers

Papers on Shimura varieties

Integral models for Shimura varieties with parahoric level structure II (with G. Pappas and R. Zhou)

The Northcott property for the isogeny class of an abelian variety  (with L. Mocz)

The stable trace formula for Shimura varieties of Abelian type  (with S.W. Shin and Y. Zhu)

Essential dimension via prismatic cohomology   (with B. Farb and J. Wolfson) -- Duke Math J., to appear

Finiteness of reductions of Hecke orbits   (with J. Lam, A. Shankar, and P. Srinivasan) -- Journal of the European Math. Soc., to appear

Independence of ℓ for Frobenius conjugacy classes associated with Abelian varieties   (with R. Zhou).

Modular functions and resolvent problems   (with B. Farb and J. Wolfson, with an appendix by N. Harman) -- Math. Ann 386 (2023), no. 1-2, 113-150.

The essential dimension of congruence covers   (with B. Farb and J. Wolfson) -- Compositio Math. 157 (2021), no. 11, 2407-2432.

Honda-Tate Theory for Shimura varieties  (with K. Madapusi Pera and S.W. Shin) -- Duke Math. J. 171 (2022), no. 7, 1559-1614.

Integral models for Shimura varieties with parahoric level structure (with G. Pappas) -- Publicationes Math IHES, 128 (2018), 121 - 218.

Mod p points on Shimura varieties of abelian type -- J.A.M.S. 30 (2017) 819-914.

Connected components of affine Deligne-Lusztig varieties in mixed characteristic (with M. Chen and E. Viehmann) -- Compositio Math., 151 (2015), no. 9, 1697-1762.

Integral models for Shimura varieties of abelian type  -- J.A.M.S. 23(4) (2010), 967-1012.

The Grothendieck-Katz conjecture for certain locally symmetric varieties  (with B. Farb) -- IMRN 22 (2009) 4159-4167.

Integral canonical models of Shimura varieties  (notes for Journees Arithmetiques 2007) -- J. Th. Nombres Bordeaux 21(2) (2009), 301-312.


Papers on Galois representations and modular forms

Memories of Jean-Marc and his mathematics -- Gaz. Math. No. 162 (2019), 18–20.

The Breuil-Mezard conjecture for potentially Barsotti-Tate representations (with T. Gee) -- Forum of Mathematics Pi, 2 (2014), e1, 56 pp.

The structure of potentially semi-stable deformation rings -- Proceedings of ICM 2010,Vol. II, 294-311.

Galois representations and Lubin-Tate groups  (with W. Ren) -- Documenta Math. 14 (2009), 441-461.

Deformations of GQp and GL2(Qp) representations  --  Astérisque 330, (2010), 529-542.

What is a Galois representation ?  -- Notices of the AMS 54 (2007), 718-719.

Modularity of 2-adic Barsotti-Tate representations -- Invent. Math. 178(3) (2009), 587-634.
 
The Fontaine-Mazur conjecture for GL2  -- J.A.M.S. 22(3) (2009) 641-690.

Potentially semi-stable deformation rings  -- J.A.M.S. 21(2) (2008), 513-546.

Modularity of 2-dimensional Galois representation  -- Current Developments in Mathematics 2005, 191-230.

Modularity of some geometric Galois representations (with an appendix by O.Gabber) -- L-functions and Galois representations (Durham 2004), 438-470.

Crystalline representations and F-crystals  --  Algebraic Geometry and Number Theory, Drinfeld 50th Birthday volume,  459-496.

Moduli of finite flat group schemes and modularity -- Annals of Math. 170(3) (2009), 1085-1180.

Locally analytic cuspidal representations for GL2 and related groups  (with M.Strauch) -- J. Inst. Math. Jussieu 5(3) (2006), 373-421.

Geometric deformations of modular Galois representations -- Invent. Math. 157(2) (2004), 275-328.

Overconvergent modular forms and the Fontaine-Mazur conjecture -- Invent. Math. 153(2) (2003), 373-454.

A Note on Artin Motives    (with S. Wortmann) -- Math. Res. Lett. 10 (2003) no. 2-3, 375-389.

Potential semi-stability of p-adic étale cohomology -- Israel J. Math. 129 (2002), 157-174.

Overconvergent Hilbert Modular forms  (with K.F. Lai) -- Amer. J. Math 127 (2005), 735-783.


Papers on unit F-crystals

An introduction to the Riemann-Hilbert correspondence for unit F-crystals     (with M. Emerton) -- Geometric aspects of Dwork theory II, 677-700 (2004).

A Riemann-Hilbert correspondence for unit F-crystals  I  and  II     (with M. Emerton) --  Astérisque, 293 (2004).

Unit L-functions and a conjecture of Katz    (with M. Emerton) -- Ann. of Math. (2) 153 (2001) no. 2, 329-354.
 

Papers on Log. Schemes

Endomorphisms of log. schemes  -- Rend. Sem. Mat. Univ. Padova 109 (2003) I, 247-281.

Prime to p fundamental groups and tame Galois actions -- Ann. Inst. Fourier 50 (4) (2000), 1099-1126.
 

Papers with a rigid or complex analytic flavour

Local constancy in non-abelian families of Galois representations -- Math. Z. 233 (2000), 347-363.

Local constancy in p-adic families of Galois representations -- Math. Z. 230 (1999), 569-593.

Analytic functions on Zariski open sets, and local cohomology -- J. Reine Angew. Math.506 (1999), 117-144.
 

Other Papers

D-modules and finite monodromy   (with H. Esnault) -- Selecta Math. (N.S.) 24 (2018), no. 1, 145–155.

Eigenvalues of Frobenius and Hodge numbers  (with G. Lehrer) -- Q.J. Pure and Appl. Math., issue in honour of John Coates, 2(2) (2006), 497-518.

Equivariant Poincare polynomials and counting points in characteristic p    (with G. Lehrer) -- J. Algebra 247 (2002) no. 2, 435--451.


 

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