Professor
Ph.D., 1994, Princeton University
At Binghamton since 2007

Areas of interest: Arithmetic Algebraic Geometry
Summary of research interests

 E-mail: adrian@math.binghamton.edu Phone: (607)-777-6036 Fax: (607)-777-2450

• Office: WH 111
• Office hours:  T 1:15-2:45 W 3:30-5:00
• Courses:
• Fall 2016  Math 507 Section 01: Linear Algebra and Matrix Theory MWF 9:40 - 10:40 WH-100E

• Ph. D. Students:
• Ding Ding, Fall, 2015
Thesis: Canonical Barsotti - Tate Groups of Level m
• Jinghao Li, Spring, 2015
Thesis: Purity Results on F-crystals
• Xiao Xiao, Spring, 2011
Thesis: Invariants of F-crystals

CV
ARITHMETIC SEMINAR AT BINGHAMTON
ALGEBRA SEMINAR AT BINGHAMTON

# MATHEMATICAL GENEALOGY

In zero steps from (i.e., born to) Angela Vasiu.
In one step from Gerd Faltings.
In two steps from Hans-Joachim Nastold.
In three steps from Friedrich Karl Schmidt.
In four steps from Alfred Loewy.
In five steps from C. L. Ferdinand (Carl Louis) Lindemann and Gustav A. Bauer.
In six steps from Felix Klein.
In seven steps from Julius Plücker and Rudolf Otto Sigismund Lipschitz.
In eight steps from Christian Ludwig Gerling and Gustav Peter Lejeune Dirichlet and Martin Ohm.
In nine steps from Carl Friedrich Gauß and Simeon Denis Poisson and Jean-Baptiste Joseph Fourier and Karl Christian von Langsdorf.
In ten steps from Johann Friedrich Pfaff and Joseph Louis Lagrange and Pierre-Simon Laplace and Abraham Gotthelf Kästner.
In eleven steps from and Johann Elert Bode and Leonhard Euler and Jean Le Rond d'Alembert and Christian August Hausen.
In twelve steps from Johann Georg Büsch and Johann Bernoulli and Johann Christoph Wichmannshausen and Johann Andreas Planer.
In thirteen steps from Jacob Bernoulli ...
In fourteen steps from Gottfried Wilhelm Leibniz ...

# PAPERS ON REDUCTIVE GROUP SCHEMES, CRYSTALLINE THEORIES, AND SHIMURA VARIETIES

1. Integral canonical models of Shimura varieties of preabelian type,
Asian J. Math. 3 (1999), no. 2, 401--517
pdf
1+. Integral canonical models of Shimura varieties of preabelian type,
fully corrected version, 135 pages
pdf
2. Surjectivity criteria for p-adic representations, Part I,
Manuscripta Math. Vol. 112 (2003), no. 3, 325--355
doi
3. A purity theorem for abelian schemes,
Michigan Math. J. 52 (2004), no. 1, 71--82
doi
4. Surjectivity criteria for p-adic representations, Part II,
Manuscripta Math. Vol. 114 (2004), no. 4, 325--355
doi
5. On two theorems for flat, affine groups schemes over a discrete valuation ring,
Centr. Eur. J. Math. 3 (2005), no. 1, 14--25
pdf
6. Unipotent, normal subgroup schemes of reductive groups,
C. R. Acad. Sci. Paris, Ser. I 341 (2005), no. 2, 79--84
pdf
7. Crystalline boundedness principle,
Ann. Sci. Ec. Norm. Sup. 39 (2006), no. 2, 245--300
pdf
8. Traverso's isogeny conjecture for p-divisible groups (with M.-H. Nicole),
Rend. Semin. Mat. U. Padova 118 (2007), 73--83
arXiv
9. Projective integral models of Shimura varieties with compact factors,
J. Reine Angew. Math. 618 (2008), 51--75
pdf
10. Minimal truncations of supersingular p-divisible groups (with M.-H. Nicole),
Indiana Univ. Math. J. 56 (2007), no. 6, 2887--2897
doi
11. Level m stratifications of versal deformations of p-divisible groups,
J. Alg. Geom. 17 (2008), no. 4, 599--641
arXiv
12. Integral canonical models of unitary Shimura varieties,
Asian J. Math. 12 (2008), no. 2, 151--176
pdf
13. Some cases of the Mumford--Tate conjecture and Shimura varieties,
Indiana Univ. Math. J. 57 (2008), no. 1, 1--75
doi
14. Geometry of Shimura varieties of Hodge type over finite fields,
Proceedings of the NATO Advanced Study Institute on {\it Higher dimensional geometry over finite fields}, G\"ottingen, Germany (June 25 - July 06, 2007), 197--243, NATO Science for Peace and Security Series, D: Information and Communication Security - Vol. 16, IOS Press, 2008
arXiv
15. On the Tate and Langlands--Rapoport conjectures for Shimura varieties,
Oberwolfach Reports 5 (2008), no. 3, 2015--2018, Report No. 35/2008, Arithmetic Algebraic Geometry Workshop (organized by G. Faltings, J. de Jong, R. Pink), Mathematisches Forschungsinstitut Oberwolfach, Germany, August 3--8, 2008
xxx.mfo.de
16. Reconstructing p-divisible groups from their truncations of small level,
Comment. Math. Helv. 85 (2010), no. 1, 165--202
arXiv pdf
17. Breuil's classification of p-divisible groups over regular local rings of arbitrary dimension (with Thomas Zink),
Advanced Studies in Pure Mathematics 58 (2010), 461--479, Proceeding of Algebraic and Arithmetic Structures of Moduli Spaces, Hokkaido University, Sapporo, Japan, 2007
pdf
18. Mod p classification of Shimura F-crystals,
Math. Nachr. 283 (2010), no. 8, 1068--1113
arXiv doi
19. Purity of level m stratifications (with Marc-Hubert Nicole and Torsten Wedhorn)
Ann. Sci. Ec. Norm. Sup. 43 (2010), no. 6, 925--955
arXiv
20. Purity results for p-divisible groups and abelian schemes over regular bases of mixed characteristic (with Thomas Zink),
Doc. Math. 15 (2010), 571--599
pdf
21. Deformation subspaces of p-divisible groups as formal Lie group structures associated to p-divisible groups,
J. Alg. Geom., Vol. 20 (2011), no. 1, 1--45
arXiv
22. Manin problems for Shimura varieties of Hodge type,
J. Ramanujan Math. Soc. 26 (2011), no. 1, 31--84
arXiv
23. A motivic conjecture of Milne,
J. Reine Agew. Math. (Crelle) 685 (2013), 181--247
arXiv online
24. Integral models in mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part I,
J. Ramanujan Math. Soc. 27 (2012), no. 4, 425--477
pdf
25. Boundedness results for finite flat group schemes over discrete valuation rings of mixed characteristic (with Thomas Zink),
J. Number Theory 132 (2012), no. 9, 2003--2019
pdf doi
26. Generalized Serre--Tate ordinary theory,
International Press of Boston, Inc., 243 pages, ISBN: 978-1-57146-277-0
book
27. Dimensions of group schemes of automorphisms of truncated Barsotti--Tate groups (with Ofer Gabber),
Int. Math. Res. Not. IMRN 2013, no. 18, 4285-4333
pdf doi
28. Subtle invariants for p-divisible groups and Traverso's conjectures,
Oberwolfach Reports 9 (2012), no. 3, 2363--2366, Report No. 38/2012, Arithmetic Algebraic Geometry Workshop (organized by G. Faltings and J. de Jong), Mathematisches Forschungsinstitut Oberwolfach, Germany, August 5--11, 2012
pdf
29. Stratifications of Newton polygon strata and Traverso's conjectures for $p$-divisible groups (with Eike Lau and Marc-Hubert Nicole)
Annals of Mathematics 178 (2013), no. 3, 789--834
pdf online
30. Integral models in mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part II,
Math. Nachr. 287, No. 14--15, 1756--1773 (2014)
pdf doi
31. Extension theorems for reductive group schemes,
Algebra \& Number Theory Vol. 10 (2016), 89--115
pdf

# NEW MANUSCRIPTS

1. Extension theorems for reductive group schemes
33 pages, September 28, 2015 (longer version of Paper 31 above; its second part is to be splitted out)
pdf
2. Isogeny and symmetry properties for Barsotti--Tate groups (joint work with Ofer Gabber)
34 pages, August 4, 2015
pdf

# OLD MANUSCRIPTS

1. CM-lifts of isogeny classes of Shimura F-crystals over finite fields
62 pages, June 19, 2012
pdf
2. Moduli schemes and the Shafarevich conjecture (the arithmetic case) for pseudo-polarized K3 surfaces
46 pages
pdf
3. Good reductions of Shimura varieties of Hodge type in arbitrary mixed characteristic, Part I,
56 pages, September 6, 2016
arXiv
4. Good reductions of Shimura varieties of Hodge type in arbitrary mixed characteristic, Part II,
29 pages, July 24, 2012
arXiv
5. On the Tate and Langlands--Rapoport conjectures for special fibres of integral canonical models of Shimura varieties of abelian type
55 pages, October 17, 2012
arXiv
6. Three methods to prove the existence of integral canonical models of Shimura varieties of Hodge type
15 pages
pdf

# COURSES

1. Math 507: Linear Algebra and Matrix Theory, Section 1
pdf
2. Math 375: Complex Variables, Section 2 (Spring 2017, tentative file)
pdf

# NOTES

1. Letter from Deligne (to Kisin with CC to us)
08/26/2011
pdf
2. Letter from Gabber to Ogus
7/22/1992
pdf
3. Points of integral canonical models of preabelian type, p-divisible groups, and applications
third part, 8/26/99
ps
4. Shimura varieties and the Mumford-Tate conjecture
part two, 2/3/00
pdf

# OLDER VERSIONS OF SOME OF THE PAPERS AND MANUSCRIPTS

1. Points of integral canonical models of preabelian type, p-divisible groups, and applications
part one
ps
2. Points of integral canonical models of preabelian type, p-divisible groups, and applications
part one, 12/99
ps
3. Shimura varieties and the Mumford-Tate conjecture
ps
4. Shimura varieties and the Mumford-Tate conjecture
Older version
ps
5. Points of integral canonical models of preabelian type, p-divisible groups, and applications
part 2A
ps
6. Points of integral canonical models of preabelian type, p-divisible groups, and applications
part 2A, 1/19/2000
ps
Points of integral canonical models of preabelian type, p-divisible groups, and applications
part 2C, 1/31/00, p. 1--104
ps
7. A supplemnet to "Points of integral canonical models of preabelian type, p-divisible groups, and applications
part 2C, 1/31/00, p. 1--104", 2/2/00
ps

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