João Pedro dos Santos

Academic address

Education and Curriculum

Research interests

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

Scientific publications

• Algebraic theory of formal regular-singular connections with parameters. July 2021. With P. H. Hai and Pham Thanh Tam. The slides from a lecture at the AGEA seminar cover parts of this work.


• Connections on trivial vector bundles over projective schemes. June 2021. With I. Biswas and P. H. Hai. Some slides related to this work.


• On certain Tannakian categories of integrable connections over Kähler manifolds. With I. Biswas, S. Dumitrescu and S. Heller. Canadian Jour. of Mathematics, Online version.


• Regular-singular connections on relative complex schemes. With P. H. Hai. Version 1, February 2020. Version 2, June 2020. Slides from a lecture at the AGEA seminar covering parts of this work.


• Finite torsors on projective schemes defined over a discrete valuation ring. With P. H. Hai. Version 1, April 2019. Manuscript notes for a seminar in Rennes.


• On the fundamental group schemes of certain quotient varieties. With I. Biswas and P. H. Hai. Version 1, June 2018. Version 2, May 2019. Version 3, April 2020. To appear in Tohoku Math. Journal.


• On the structure of affine flat group schemes over discrete valuation rings, II. With P. H. Hai. International Mathematics Research Notices, Volume 2021, Issue 12, June 2021, 9375–9424. Online version.


• On the structure of affine flat group schemes over discrete valuation rings, I. 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 etale 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. DOI


• 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), 535--590.


• Habilitation à diriger des recherches. 2014, Université de Paris 6.


• On the number of Fronebius trivial vector bundles on specific curves. Archiv der Mathematik. Septembre 2012, Volume 99, Issue 3, pp 227-235.


• Vector bundles trivialized by proper morphisms and the fundamental group scheme, II. With I. Biswas. The Arithmetic of fundamental groups, PIA 2010, 77--88. Contrib. Math. Comput. Sci., 2, Springer, Heidelberg, 2012.


• 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.


• 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 Soc. Math. 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. Preprint 2008.


• The behaviour of the differential Galois group on the generic and special fibres: A Tannakian approach. J. reine angew. Math. 637 (2009), 63--98.


• Fundamental group-schemes in positive characteristic. Based on a talk delivered at "Arithmetic and differential Galois groups", Oberwolfach, May 2007. Oberwolfach reports Volume 4, Issue 2, 1514--1516 (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.

Also of interest

• Hints on mathematical writing by D. Goss
  
• A note on Frobenius divided modules in mixed characteristics by Pierre Berthelot. Bull. Soc. Math. France 140 (2012), no. 3, 441–458.
• The DOI

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