y Adrian Vasiu, Home Page

MATHEMATICAL GENEALOGY OF ADRIAN VASIU
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 Plucker 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 Kastner.
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 Busch 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 OF ADRIAN VASIU 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 		pdf 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		 pdf 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 doi
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 doi
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		 numdam
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 doi
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 doi
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 doi
32. Purity of crystalline strata (joint work with Jinghao Li),
24 pages, Tunis. J. Math. 1 (2019), no. 4, 519--538		 pdf doi
33. Good reductions of Shimura varieties of Hodge type in arbitrary mixed characteristic. Part I,
Math. Nachr. 293 (2020), no. 12, 2399--2448		 pdf doi
34. Purity for Barsotti--Tate groups in some mixed characteristic situations (joint work with Ofer Gabber),
Algebr. Geom. 8 (2021), no. 4, 490--517		 pdf
35. On Lie algebra modules which are modules over semisimple group schemes (joint work with Micah Loverro),
29 pages, to appear in Manuscripta Math.		 pdf doi
36. Waring Problem for Matrices over Finite Fields (joint work Krishna Kishore and Sailun Zhan),
J. Pure Appl. Algebra 228 (2024), no. 7, Paper No. 107656.		 pdf doi

NEW MANUSCRIPTS OF ADRIAN VASIU
1. On matrix invertible completions over commutative rings (joint work with Grigore Calugareanu and Horia F. Pop),
45 pages, March 15, 2023		 pdf
2. The δ-invariant theory of Hecke correspondences on Ag (joint work with Alexandru Buium)
242 pages, August 2, 2022		 pdf
3. The classification of p-quasi-healthy henselian regular local rings of dimension 2 (joint work with Ofer Gabber)
44 pages, July 2, 2020 		pdf
4. Isogeny and symmetry properties for Barsotti--Tate groups (joint work with Ofer Gabber)
35 pages, August 27, 2018		 pdf

OLD MANUSCRIPTS OF ADRIAN VASIU
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, September 24, 1999		 pdf
3. Good reductions of Shimura varieties of Hodge type in arbitrary mixed characteristic, Part II,
29 pages, July 24, 2012		 arXiv
4. 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
5. Three methods to prove the existence of integral canonical models of Shimura varieties of Hodge type
15 pages		 pdf

COURSES OF ADRIAN VASIU
1. Math 304: Linear Algebra, Section 3
 pdf
2. Math 479: Advanced Calculus of Several Variables, Section 1
 pdf
3. Math 330: Number Systems, Section 1
 pdf
4. Math 401: Modern Algebra I, Section 2
 pdf

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

OLDER VERSIONS OF SOME OF THE PAPERS AND MANUSCRIPTS OF ADRIAN VASIU
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