Joao Pedro's Home Page

João Pedro P. dos Santos

$JP_2014$

Academic address:
Institut de Mathématiques de Jussieu
Case 247 -- 4, Place Jussieu
75252 Paris Cedex
France
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

CV

$Madonna del Velo$

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:

Regular-singular connections on relative complex schemes. With P. H. Hai. Version 1, February 2020.

Finite torsors on projective schemes defined over a discrete valuation ring. With P. H. Hai. Version 1, April 2019.

On the fundamental group schemes of certain quotient varieties. With I. Biswas and P. H. Hai. Version 1, June 2018. Version 2, May 2019.

On the structure of affine flat group schemes over discrete valuation rings, II. With P. H. Hai. Version 1, September 2017. Version 2, February 2018. Version 3, October 2018. Version 4, February 2019.

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. Version 4, January 2018. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XVIII (2018), 977-1032.

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. Version 2, May 2017. Version 3, February 2018. Math. Nachrichten Vol. 291, Issue11-12. August 2018, 1733–1742. https://doi.org/10.1002/mana.201600494

Abelianization of the F-divided fundamental group scheme. With I. Biswas. Proc. Indian Acad. Sci. Math. Sci. 127 (2017), no. 2, 281--287.

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
http://dx.doi.org/10.1016/j.crma.2009.09.006

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 Volume 4, Issue 2, 1514--1516 (2007). (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. http://www.math.univ-montp2.fr/~bruguieres/recherche.html

Enseignement

Last update : 15.02.2020