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Prof Mohamed Saidi

Professor of Pure Mathematics

 M.Saidi@exeter.ac.uk

 (Streatham) 5277

 01392 725277

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Overview

  • Born in Algiers (Algeria).
  • Algerian citizenship (only). 
  • Attended school, junior school, and High school in Algeria.
  • Graduated from Constantine university in Mathematics (option analysis) (Jun 1990).
  • DEA in Pure Mathematics from Universitie Bordeaux I. Mention tres bien (Sep 1991).
  • PhD in Pure Mathematics from Universitie Bordeaux I under the supervision of Prof. Michel Matignon. Mention felicitations des membres du jury (Jun 1994).
  • Post-Doc at Munster University (Germany), with Prof. S. Bosch, (Sep 1994 - Sep 1995).
  • Post-Doc at the Max-Planck Institut for Mathematics in Bonn (Germany) (Oct 1994 - Dec 1994).
  • Post-Doc at Heidelberg university (Germany), with Prof. B.H.Matzat (Jun 1996- Aug 1997).
  • Post-Doc at Bonn-University (Germany), with Prof. F.Pop, (Sep 1997 - Jul 1999).
  • Visiting Professor at Stellenbosch University (South Africa) (Aug 1998 - Sep 1998).
  • Post-Doc at MSRI (Berkley), special Galois semester, (Aug 1999 - Dec 1999).
  • Lecturer in Pure Mathematics at Durham University (UK) (Jan 2000 - Jul 1004).
  • Visiting Professor at the Max-Planck-Institut for Mathematics in Bonn (Germany), (Mar 2003 - Jun 2004).
  • Reader at Exeter University (Jul 2004 onwards).
  • Visiting Professor at the Research Institut for Mathematical Sciences (Kyoto university), (Sep 2005 - Oct 2006).
  • Associate Professor at Exeter University (2007).
  • Profossor of pure mathematics at Exeter university (2015).
  • I regularly visit the Research Institute for Mathematical Sciences at Kyoto university (RIMS) as an invited professor (for a period of three months), recent visits include the summers 2019-2018-2017-2016-2014-2013-2012-2011.
  • I occasionally visit the Max-Planck-Institute for Mathematical Sciences in Bonn as an invited researcher, recent visits include: 10/2019-03/2020, and 02/2015-05/2015.

Languages: Arabic, French, English, German, some basic Japanese.

Research Interests

I am interested in several research areas related to arithmetic geometry, algebraic geometry and number theory. I am especially interested in questions and problems related to algebraic and arithmetic fundamental groups over various fields of interest: fields of positive characteristics, finite fields, finitey generated fields, and p-adic local fields. These include:

  • The anabelian geometry of curves over finite, p-adic, and number fields .
  • The anabelian geometry of finitely generated fields.
  • Sections of arithmetic fundamental groups.
  • Arithmetic fundamental groups and Diophantine geometry.
  • Local-global principles for torsors under fundamental groups.
  • Structure of fundamental groups in positive characteristics.
  • Etale fundamental groups of rigid analytic varieties.
  • Arithmetic of abelian varieties over finitely generated fields.
  • Arithmetic of rigid analytic p-adic varieties.
  • Liftings and degeneration of covers of curves, semi-stable reduction of covers of arithmetic curves.
  • Ramification theory.

Recent Research Achievements

  • Together with my collaborator Akio Tamagawa we established a far reaching refined version of the Grothendieck anabelian conjecture for hyperbolic curves over finite fields.
  • Recently we established a much refined version of the Grothendieck birational anabelian conjecture for finitely generated fields.
  • We also proved that the structure of the geometric fundamental group is not constant in a non-isotrivial family of curves in positive characteristics.
  • Together with (my former PhD student) Mike Tyler we proved that the birational Grothendieck section conjecture holds true over finitely generated fields if it holds true over number fields.
  • Initiated the theory of cuspidalisation of sections of arithmetic fundamental groups in the search of rational points.
  • Proved new results regarding the structure of geometric etale fundamental groups of affinoid p-adic curves.
  • Established a local-global principle for torsors under prosolvable fundamental groups.
  • Found new examples of non-geometric sections of arithmetic fundamental groups.

Teaching Interests

I have an experience in teaching the following courses :

  • Number theory.
  • Real analysis.
  • Complex analysis.
  • p-adic numbers.
  • Algebra.
  • Group, Rings, and Fields.
  • Algebraic curves.
  • Representation of finite groups.

Other Relevant Information

  • I have been awarder an Advanced EPSRC Fellowship Oct 2002 - Sep 2007.
  • I am co-organizing with John Coates, Peter Schneider, Minhyong Kim and Florian Pop a special semester at the Isaac Newton Institute for Mathematical Sciences in Cambridge on "Non-abelian Fundamental Groups in Arithmetic Geometry" from Jul - Dec 2009, for more details, see: http://www.newton.cam.ac.uk/programmes/NAG/index.html
  • Refereed papers for several research journals: the American Journal of Mathematics, Mathematishe Annalen, Publication of RIMS kyoto university, Compositio, Journal of Algebra.
  • I have been external examiner in PHD examinations.

Qualifications PhD in Pure Mathematics

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Publications

Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.

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2023

2022

2021

2020

2019

2018

2017

2016

2015

  • Saidi M, Williams N. (2015) On the existence of a torsor structure for Galois covers over a complete discrete valuation ring. [PDF]

2014

2013

  • Saïdi M. (2013) On the existence of non-geometric sections of arithmetic fundamental groups, Mathematische Zeitschrift, pages 1-12.
  • Saïdi M. (2013) On the p-adic section conjecture, Journal of Pure and Applied Algebra, volume 217, no. 3, pages 583-584, DOI:10.1016/j.jpaa.2012.08.002.

2012

  • Saidi M. (2012) On the birational anabelian section conjecture. [PDF]
  • Saidi M. (2012) Fake liftings of Galois covers between smooth curves, Galois-Teichmuller theory and arithmetic geometry, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, 457-501.
  • Saïdi M. (2012) On the p-adic section conjecture, Journal of Pure and Applied Algebra.
  • Saidi M. (2012) The cuspidalisation of section of arithmetic fundamental groups, Advances in Mathematics, volume 230, DOI:10.1016/j.aim.2012.04.002.
  • Saidi M. (2012) On a Theorem of Garuti, Journal of pure and applied algebra, volume 216, pages 1235-1244, DOI:10.1016/j.jpaa.2011.10.001.

2011

  • Saidi M, Coates J, Kim M, Pop F, Schneider P. (2011) Non abelian fundamental groups and Iwasawa theory, London Mathematical Society Lecture Notes Series.

2010

  • Saidi M. (2010) Good Sections of Arithmetic Fundamental Groups. [PDF]

2009

  • Saidi M, Tamagawa A. (2009) On the Anabelian Geometry of Hyperbolic Curves over Finite Fields, RIMS Kokyuroku Bessatsu, no. B12, pages 67-89.
  • Saidi M. (2009) On the anabelian geometry of hyperbolic curves over finite fields, Fukoka University, 26th - 28th Aug 2008.
  • Saidi M, Tamagawa, A. (2009) A prime-to-p Version of Grothendieck's Anabelian Conjecture for Hyperbolic Curves over Finite Fields of Characteristic p>0, Publications of the Reserach Institute for Mathematical sciences Kyoto University, volume 45, no. 1, pages 135-186. [PDF]

2007

  • Saidi M. (2007) On the degeneration of étale $\bold Z/p\bold Z$ and $\bold Z/p\sp 2\bold Z$-torsors in equal characteristic $p>0$. Hiroshima Math. J. 37 (2007), no. 2, 315--341, Hiroshima Math. J, volume 37, no. 2, pages 315-341. [PDF]
  • Saidi M. (2007) On the degeneration of etale Z/pZ and Z/p2Z-torsors in equal characteristic p > 0, HIROSHIMA MATHEMATICAL JOURNAL, volume 37, no. 2, pages 315-341, DOI:10.32917/hmj/1187916322. [PDF]
  • Saidi M. (2007) On a thorem of Uchida on isomorphisms between galois groups of function fields, Number theory conference at Chuo university.
  • Saidi M. (2007) Galois covers of degree $p$ and semi-stable reduction of curves in mixed characteristics, Publ. Res. Inst. Math. Sci. Kyoto university, volume 43, no. 3, pages 661-684, DOI:10.2977/prims/1201012037.
  • Saidi M. (2007) Galois covers of degree $p$ and semi-stable reduction of curves in equal characteristic $p>0$, Math. J. Okayama Univ, volume 49, pages 113-138. [PDF]

2005

2004

2003

  • Saidi M. (2003) Torsors under finite and flat groups schemes of rank p, with Galois action, DOI:10.1007/s00209-003-0566-3.
  • Mohamed, S.. (2003) On the specialisation homorphism between fundamental groups in positive characteristics, Mathematical Science Research Institute Publication, volume 41, pages 107-118.
  • Mohamed, S.. (2003) Torsors under finite and flat groups schemes of rank p, with Galois action, Mathematische Zeitschrift, volume 245, no. 4, pages 695-710.
  • Saidi M. (2003) On the specialisation homomorphism between fundamental groups of curves in positive characteristics, Galois Groups and Fundamental Groups, Cambridge University Press, 107-118.

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