## Prof Mohamed Saidi

#### Professor of Pure Mathematics

**(Streatham) 5277**

**01392 725277**

## 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

## 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.}

| 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2007 | 2005 | 2004 | 2003 |

### 2023

- Saidi M. (2023) Local sections of arithmetic fundamental groups of p-adic curves. [PDF]
- Saidi M. (2023) Local sections of arithmetic fundamental groups of p-adic curves,
*Nagoya Mathematical Journal*, DOI:10.1017/nmj.2023.33. [PDF] - Corato A, Saïdi M. (2023) The m-step Solvable Hom-Form of Birational Anabelian Geometry for Number Fields. [PDF]
- Saidi M. (2023) Further examples of non-geometric sections of arithmetic fundamental groups,
*Publications of the Research Institute for Mathematical Sciences*, volume 59, DOI:10.4171/PRIMS/59-3-5. [PDF]

### 2022

- Corato A. (2022) Homomorphusm.
- Corato A. (2022) The Homomorphism Form of Birational Anabelian Geometry.
- Saidi M. (2022) On sections of arithmetic fundamental groups of open p-adic annuli. [PDF]
- Saidi M. (2022) ON SECTIONS OF ARITHMETIC FUNDAMENTAL GROUPS OF OPEN p-ADIC ANNULI,
*Comptes Rendus Mathématique*, volume 235, pages 465-483, DOI:10.1016/j.jnt.2021.07.006. [PDF] - Saïdi M, Tamagawa A. (2022) The m-step solvable anabelian geometry of number fields,
*Journal für die reine und angewandte Mathematik*, volume 2022, no. 789, pages 153-186, DOI:10.1515/crelle-2022-0025. [PDF]

### 2021

- Saidi M. (2021) A local-global principle for torsors under geometric prosolvable fundamental groups II,
*Journal of Number Theory*, DOI:10.1016/j.jnt.2021.07.006. - Tyler M, Saidi M. (2021) On the birational section conjecture over finitely generated field,
*Algebra and Number Theory*, volume 15: 2 2021, DOI:10.2140/ant.2021.15.435.

### 2020

- Saïdi M. (2020) Arithmetic of p-adic curves and sections of geometrically abelian fundamental groups,
*Mathematische Zeitschrift*, DOI:10.1007/s00209-020-02553-1. - Saidi M. (2020) On etale fundamental groups of formal fibres of p-adic curves,
*Tohoku Mathematical Journal*, volume 72, pages 63-76, DOI:10.2748/tmj/1585101621.

### 2019

- Saidi M, Tamagawa A. (2019) The $m$-step solvable anabelian geometry of number fields. [PDF]
- Saïdi M. (2019) The cuspidalisation of sections of arithmetic fundamental groups II,
*Advances in Mathematics*, volume 354, DOI:10.1016/j.aim.2019.106737.

### 2018

- Saidi M, Tamagawa A. (2018) On the arithmetic of abelian varieties,
*Journal fur die Reine und Angewandte Mathematik*, volume 2020, pages 1-33, DOI:10.1515/crelle-2018-0024. [PDF] - Saidi M, Tamagawa A. (2018) A refined version of Grothendieck's anabelian conjecture for hyperbolic curves over finite fields,
*Journal of Algebraic Geometry*, volume 27, pages 383-448, DOI:10.1090/jag/708. - Saïdi M. (2018) Étale fundamental groups of affinoid P-adic curves,
*Journal of Algebraic Geometry*, volume 27, no. 4, pages 727-749, DOI:10.1090/jag/707. - Saïdi M, Williams N. (2018) Galois covers of type (P, · · ·, p), vanishing cycles formula, and the existence of torsor structures,
*Osaka Journal of Mathematics*, volume 55, no. 2, pages 259-296.

### 2017

- Saïdi M, Tamagawa A. (2017) A refined version of Grothendieck's birational anabelian conjecture for curves over finite fields,
*Advances in Mathematics*, volume 310, pages 610-662, DOI:10.1016/j.aim.2017.02.010.

### 2016

- Saidi M. (2016) On the section conjecture over function fields and finitely generated fields,
*Publications of the Research Institute for Mathematical Sciences*. - Saidi M, Tamgawa A. (2016) Variation of fundamental groups of curves in positive characteristics,
*Journal of Algebraic Geometry*, volume 26, pages 1-16, DOI:10.1090/jag/665.

### 2015

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

### 2014

- Saïdi M. (2014) A local-global principle for torsors under geometric prosolvable fundamental groups,
*Manuscripta Mathematica*. - Saïdi M. (2014) On the existence of non-geometric sections of arithmetic fundamental groups,
*Mathematische Zeitschrift*, volume 277, no. 1-2, pages 361-372, DOI:10.1007/s00209-013-1260-8.

### 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/
*p*Z and Z/*p*^{2}Z-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

- Saidi M. (2005) On complete families of curves with a given fundamental group in positive characteristics,
*Manuscripta Mathematica*, volume 118, no. 4, pages 425-441, DOI:10.1007/s00229-005-0592-z.

### 2004

- Saidi M. (2004) Wild ramification and a vanishing cycles formula,
*Journal of Algebra*, volume 273, no. 1, pages 108-128, DOI:10.1016/S0021-8693(03)00288-6.

### 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.