João Pedro P. dos Santos                                                                                                                                                                                       

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Institut de Mathématiques de Jussieu   
Case 247 -- 4, Place Jussieu
75252 Paris Cedex
Tel: +33 (0) 1 44 27 90 12

(2014) Habilitation à diriger des recherches, Institut de Mathématiques de Jussieu - Paris Rive Gauche, Université de Paris 6
(2006) PhD in Mathematics, DPMMS, University of Cambridge
(2003) Certificate of advanced Study in Mathematics, DPMMS, University of Cambridge
(2002) MS in Pure Mathematics, IMPA



Madonna del Velo

Research interests:

Arithmetic algebraic Geometry;  D-modules in positive and mixed characteristic; differential Galois theory; fundamental group-schemes in algebraic Geometry; vector bundles; rigid analytic Geometry; Tannakian categories.

Research articles:

On the structure of affine flat group schemes over discrete valuation rings. With N. D. Duong and P. H. Hai.  Version 1, September 2015. Version 3, January 2017. To apear in Ann. Scuola Normale Superiore di Pisa.

The action of the étale fundamental group scheme on the connected component of the essentially finite one. With P. H. Hai. Version 1, November 2016.

Abelianization of the F-divided fundamental group scheme. With I. Biswas. To appear in Procedings Indian Academy of Sciences (Math. Sci.).

The homotopy exact sequence for the fundamental group scheme and infinitesimal equivalence relations. Version 1, October 2012. Version 2, March 2014. Version  4, February 2015. Algebraic Geometry, Volume 2, Issue 5 (November 2015), pp 535-590.  

On the number of Fronebius trivial vector bundles on specific curves. Archiv der Mathematik. Septembre 2012, Volume 99, Issue 3, pp 227-235. doi:10.1007/s00013-012-0424-9.

Vector bundles trivialized by proper morphisms and the fundamental group scheme, II.  With I. Biswas. The Arithmetic of fundamental groups, PIA 2010. Contributions in Mathematical and Computational Sciences. Volume 2, 2012, pp. 77--88. DOI: 10.1007/978-3-642-23905-2.

Vector bundles trivialized by proper morphisms and the fundamental group scheme. With. I. Biswas. Journal of the Inst. of Math. Jussieu (2011) 10(2), 225-234 doi:10.1017/S1474748010000071.

Triviality criteria for vector bundles over separably rationally connected varieties. With I. Biswas. Journal of the Ramanujan Mathematical Society (2013) Volume 28, no. 4, pp 423--442.

Lifting D-modules from positive to zero characteristic. Bulletin de la Société Mathématique de France Tome 139 Fasc. 2, 2011, 145--286.  See also Berthelot's article "A note on Frobenius divided modules in mixed characteristics" (link below).

On the vector bundles over rationally connected varieties. With I. Biswas. C. R. Acad. Sci. Paris, Mathematique, Volume 347, Issues 19-20, October 2009,  1173-1176

A note on stratified modules with finite integral differential Galois groups

The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach. (V3 11.01.09). J. reine angew. Math. 637 (2009), 63--98. doi 10.1515/CRELLE.2009.091. 

Fundamental group-schemes in positive characteristic. Oberwolfach reports 0720. (Summary of "Fundamental group schemes for stratified sheaves". Based on a talk delivered at "Arithmetic and differential Galois groups", Oberwolfach, May 2007.)

Fundamental group schemes for stratified sheaves. Journal of Algebra, Volume 317, Issue 2, pp. 691–713 (2007). 

Local solutions to positive characteristic non-Archimedean differential equations. Compositio Mathematica 143 (2007) 1465–1477.

Remark: These are not the final published versions.

Also of interest:

Hints on mathematical writing, from the webpage of D. Goss.

A note on Frobenius divided modules in mixed characteristics, by Pierre Berthelot. Bull. Soc. Math. France 140 (2012), no. 3, 441–458.

On a tannakian theorem due to Nori, by A. Bruguières.


Last update : 30.03.2017