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) -- Forum of Math Π, to appear.

The Northcott property for the isogeny class of an abelian variety  (with L. Mocz) -- Compositio Math., to appear .

The stable trace formula for Shimura varieties of Abelian type  (with S.W. Shin and Y. Zhu) -- Annals of Math. Studies, to appear.

Essential dimension via prismatic cohomology   (with B. Farb and J. Wolfson) -- Duke Math. J. 173 (2024), no. 15, 3059-3106.

Finiteness of reductions of Hecke orbits   (with J. Lam, A. Shankar, and P. Srinivasan) -- .J. Eur. Math. Soc. 27 (2025), no.4, 1447-1464.

Independence of ℓ for Frobenius conjugacy classes associated with Abelian varieties   (with R. Zhou) -- Annals of Math. 202 (2025), no 3, 1077-1156.

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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