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 HansJoachim 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 JeanBaptiste Joseph Fourier and Karl Christian von Langsdorf. 

In ten steps from Johann Friedrich Pfaff and Joseph Louis Lagrange and PierreSimon 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, 401517 

1+. Integral canonical models of Shimura varieties of preabelian type,
fully corrected version, 135 pages 

2. Surjectivity criteria for padic representations, Part I,
Manuscripta Math. Vol. 112 (2003), no. 3, 325355 
doi  
3. A purity theorem for abelian schemes,
Michigan Math. J. 52 (2004), no. 1, 7182 
doi  
4. Surjectivity criteria for padic representations, Part II,
Manuscripta Math. Vol. 114 (2004), no. 4, 325355 
doi  
5. On two theorems for flat, affine groups schemes over a discrete valuation ring,
Centr. Eur. J. Math. 3 (2005), no. 1, 1425 

6. Unipotent, normal subgroup schemes of reductive groups,
C. R. Acad. Sci. Paris, Ser. I 341 (2005), no. 2, 7984 

7. Crystalline boundedness principle,
Ann. Sci. Ec. Norm. Sup. 39 (2006), no. 2, 245300 
doi  
8. Traverso's isogeny conjecture for pdivisible groups (with M.H. Nicole),
Rend. Semin. Mat. U. Padova 118 (2007), 7383 
arXiv  
9. Projective integral models of Shimura varieties with compact factors,
J. Reine Angew. Math. 618 (2008), 5175 

10. Minimal truncations of supersingular pdivisible groups (with M.H. Nicole),
Indiana Univ. Math. J. 56 (2007), no. 6, 28872897 
doi  
11. Level m stratifications of versal deformations of pdivisible groups,
J. Alg. Geom. 17 (2008), no. 4, 599641 
arXiv  doi  
12. Integral canonical models of unitary Shimura varieties,
Asian J. Math. 12 (2008), no. 2, 151176 

13. Some cases of the MumfordTate conjecture and Shimura varieties,
Indiana Univ. Math. J. 57 (2008), no. 1, 175 
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), 197243, NATO Science for Peace and Security Series, D: Information and Communication Security  Vol. 16, IOS Press, 2008 
arXiv  
15. On the Tate and LanglandsRapoport conjectures for Shimura varieties,
Oberwolfach Reports 5 (2008), no. 3, 20152018, Report No. 35/2008, Arithmetic Algebraic Geometry Workshop (organized by G. Faltings, J. de Jong, R. Pink), Mathematisches Forschungsinstitut Oberwolfach, Germany, August 38, 2008 
xxx.mfo.de  
16. Reconstructing pdivisible groups from their truncations of small level,
Comment. Math. Helv. 85 (2010), no. 1, 165202 
arXiv  
17. Breuil's classification of pdivisible groups over regular local rings of arbitrary dimension (with Thomas Zink),
Advanced Studies in Pure Mathematics 58 (2010), 461479, Proceeding of Algebraic and Arithmetic Structures of Moduli Spaces, Hokkaido University, Sapporo, Japan, 2007 

18. Mod p classification of Shimura Fcrystals,
Math. Nachr. 283 (2010), no. 8, 10681113 
arXiv  doi  
19. Purity of level m stratifications (with MarcHubert Nicole and Torsten Wedhorn)
Ann. Sci. Ec. Norm. Sup. 43 (2010), no. 6, 925955 
numdam  
20. Purity results for pdivisible groups and abelian schemes over regular bases of mixed characteristic (with Thomas Zink),
Doc. Math. 15 (2010), 571599


21. Deformation subspaces of pdivisible groups as formal Lie group structures associated to pdivisible groups,
J. Alg. Geom., Vol. 20 (2011), no. 1, 145 
arXiv  doi  
22. Manin problems for Shimura varieties of Hodge type,
J. Ramanujan Math. Soc. 26 (2011), no. 1, 3184 
arXiv  
23. A motivic conjecture of Milne,
J. Reine Agew. Math. (Crelle) 685 (2013), 181247 
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, 425477 

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, 20032019 
doi  
26. Generalized SerreTate ordinary theory,
International Press of Boston, Inc., 243 pages, ISBN: 9781571462770 
book  
27. Dimensions of group schemes of automorphisms of truncated BarsottiTate groups (with Ofer Gabber),
Int. Math. Res. Not. IMRN 2013, no. 18, 42854333 
doi  
28. Subtle invariants for pdivisible groups and Traverso's conjectures,
Oberwolfach Reports 9 (2012), no. 3, 23632366, Report No. 38/2012, Arithmetic Algebraic Geometry Workshop (organized by G. Faltings and J. de Jong), Mathematisches Forschungsinstitut Oberwolfach, Germany, August 511, 2012 

29. Stratifications of Newton polygon strata and Traverso's conjectures for $p$divisible groups (with Eike Lau and MarcHubert Nicole)
Annals of Mathematics 178 (2013), no. 3, 789834 
online  doi  
30. Integral models in mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part II,
Math. Nachr. 287, No. 1415, 17561773 (2014) 
doi  
31. Extension theorems for reductive group schemes,
Algebra \& Number Theory Vol. 10 (2016), 89115 
doi  
32. Purity of crystalline strata (joint work with Jinghao Li),
24 pages, Tunis. J. Math. 1 (2019), no. 4, 519538 
doi  
33. Good reductions of Shimura varieties of Hodge type in arbitrary mixed characteristic. Part I,
Math. Nachr. 293 (2020), no. 12, 23992448 
doi  
34. Purity for BarsottiTate groups in some mixed characteristic situations (joint work with Ofer Gabber),
Algebr. Geom. 8 (2021), no. 4, 490517 

35. On Lie algebra modules which are modules
over semisimple group schemes (joint work with Micah Loverro),
29 pages, to appear in Manuscripta Math. 
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. 
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 

2. The δinvariant theory of Hecke correspondences on Ag (joint work with Alexandru Buium)
242 pages, August 2, 2022 

3. The classification of pquasihealthy henselian regular local rings of dimension 2 (joint work with Ofer Gabber)
44 pages, July 2, 2020 

4. Isogeny and symmetry properties for BarsottiTate groups (joint work with Ofer Gabber)
35 pages, August 27, 2018 
OLD MANUSCRIPTS OF ADRIAN VASIU 


1. CMlifts of isogeny classes of Shimura Fcrystals over finite fields
62 pages, June 19, 2012 

2. Moduli schemes and the Shafarevich conjecture (the arithmetic case) for pseudopolarized K3 surfaces
46 pages, September 24, 1999 

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 LanglandsRapoport 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 
COURSES OF ADRIAN VASIU 


1. Math 304: Linear Algebra, Section 3 

2. Math 479: Advanced Calculus of Several Variables, Section 1 

3. Math 330: Number Systems, Section 1 

4. Math 401: Modern Algebra I, Section 2 
NOTES OF ADRIAN VASIU 


1. Letter from Deligne (to Kisin with CC to us)
08/26/2011 

2. Points of integral canonical models of preabelian type, pdivisible groups, and applications
third part, 8/26/99 
ps 
3. Shimura varieties and the MumfordTate conjecture
part two, 2/3/00 
OLDER VERSIONS OF SOME OF THE PAPERS AND MANUSCRIPTS OF ADRIAN VASIU 


1. Points of integral canonical models of preabelian type, pdivisible groups, and applications
part one 
ps 
2. Points of integral canonical models of preabelian type, pdivisible groups, and applications
part one, 12/99 
ps 
3. Shimura varieties and the MumfordTate conjecture 
ps 
4. Shimura varieties and the MumfordTate conjecture
Older version 
ps 
5. Points of integral canonical models of preabelian type, pdivisible groups, and applications
part 2A 
ps 
6. Points of integral canonical models of preabelian type, pdivisible groups, and applications
part 2A, 1/19/2000 
ps 
Points of integral canonical models of preabelian type, pdivisible groups, and applications
part 2C, 1/31/00, p. 1104 
ps 
7. A supplemnet to "Points of integral canonical models of preabelian type, pdivisible groups, and applications
part 2C, 1/31/00, p. 1104", 2/2/00 
ps 