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1. • CommentRowNumber1.
   • CommentAuthorTim_Porter
   • CommentTimeNov 29th 2010
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexDoes anyone have some good sources for Anabelian geometry? (I have a copy of Esquisses somewhere, but cannot find it!) At present a nLab search just gives one hit on our pages.

   Does anyone have some good sources for Anabelian geometry? (I have a copy of Esquisses somewhere, but cannot find it!) At present a nLab search just gives one hit on our pages.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeNov 29th 2010
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexDo you have the books edited by Schneps? You could probably find some good references there. For example: Geometric Galois Actions: Volume 1, Around Grothendieck's Esquisse d'un Programme (London Mathematical Society Lecture Note Series) (Vol 1)

   Do you have the books edited by Schneps? You could probably find some good references there. For example:

   Geometric Galois Actions: Volume 1, Around Grothendieck’s Esquisse d’un Programme (London Mathematical Society Lecture Note Series) (Vol 1)

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeNov 29th 2010
   • (edited Nov 29th 2010)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThanks. I have LMS lecture notes 200. I knew of this as Dessins d'enfant and via Malgoire etc. way back, and in fact linked that stuff up with the Jones and Singermann work in conversations with Gareth Jones and David Singermann, but am now told that there is an enormous explosion of stuff on this???? I must see if Leila Schneps webpages give more details.

   Thanks.

   I have LMS lecture notes 200. I knew of this as Dessins d’enfant and via Malgoire etc. way back, and in fact linked that stuff up with the Jones and Singermann work in conversations with Gareth Jones and David Singermann, but am now told that there is an enormous explosion of stuff on this???? I must see if Leila Schneps webpages give more details.

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeNov 29th 2010
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexSearch for the workshop 'Anabelian number theory and geometry' in 2001 - there are some [lecture notes](http://www.math.leidenuniv.nl/~psh/anab.shtml) from then.

   Search for the workshop ’Anabelian number theory and geometry’ in 2001 - there are some lecture notes from then.

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeNov 29th 2010
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItex@David. Thanks. My searches so far had not turned that up. I have been wondering what if any link there might be between my profinite algebraic homotopy methods and the analysis of these anabelian situations, and as always am having to find things out by myself (even more than is usual for a maths researcher of any type!) I attacked one of the piles in the corner of our dining-room area and have turned up more stuff by Leila on the Grothendieck-Teichmuller stuff which is related. It would be fun to write up an elementary 'seminar type' intro to Dessins for the lab but I have to prepare a talk for the WIMCS meeting in 3 weeks time, and then think of what to say in Lisbon in February (and as Urs will be in the audience, I had better be well prepared!:-)) (Actually in my search through the pile I also found stuff that I was missing on modal logics.... the trouble is all these areas look so interesting to tackle. Prioritise I tell myself. .... but then I end up with too many priorities!!!)

   @David. Thanks. My searches so far had not turned that up. I have been wondering what if any link there might be between my profinite algebraic homotopy methods and the analysis of these anabelian situations, and as always am having to find things out by myself (even more than is usual for a maths researcher of any type!) I attacked one of the piles in the corner of our dining-room area and have turned up more stuff by Leila on the Grothendieck-Teichmuller stuff which is related. It would be fun to write up an elementary ’seminar type’ intro to Dessins for the lab but I have to prepare a talk for the WIMCS meeting in 3 weeks time, and then think of what to say in Lisbon in February (and as Urs will be in the audience, I had better be well prepared!:-))

   (Actually in my search through the pile I also found stuff that I was missing on modal logics…. the trouble is all these areas look so interesting to tackle. Prioritise I tell myself. …. but then I end up with too many priorities!!!)

6. • CommentRowNumber6.
   • CommentAuthorTim_Porter
   • CommentTimeNov 29th 2010
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexPS I also started looking at Morel and Voevodsky again for potential links to my profinite stuff.... That all grew out of the Pursuing Stacks, and other manuscripts in the 1980s.!!!

   PS I also started looking at Morel and Voevodsky again for potential links to my profinite stuff…. That all grew out of the Pursuing Stacks, and other manuscripts in the 1980s.!!!

7. • CommentRowNumber7.
   • CommentAuthorTim_Porter
   • CommentTimeDec 10th 2010
   • (edited Dec 10th 2010)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexCreated a stub [[anabelian geometry]]. (Picking up from another thread... a recurrent typo for me is abelain, so if someone sees that in the Lab it is probably due to me!

   Created a stub anabelian geometry. (Picking up from another thread… a recurrent typo for me is abelain, so if someone sees that in the Lab it is probably due to me!

8. • CommentRowNumber8.
   • CommentAuthorTim_Porter
   • CommentTimeSep 18th 2012
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexAdded some cross links.

   Added some cross links.

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeSep 19th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI worked on _[[anabelian geometry]]_. Added a few paragraphs to the Idea-section and added references.

   I worked on anabelian geometry. Added a few paragraphs to the Idea-section and added references.

10. • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeSep 21st 2012
    • PermaLink
    Author: Tim_Porter
    Format: MarkdownItexThere are several uses of $\pi_1^{et}(x,X)$, rather than what I would expect namely $\pi_1^{et}(X,x)$. Is this a typo or am I missing something?

    There are several uses of $\pi_1^{et}(x,X)$, rather than what I would expect namely $\pi_1^{et}(X,x)$. Is this a typo or am I missing something?

11. • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeSep 21st 2012
    • PermaLink
    Author: Urs
    Format: MarkdownItexNot sure if its a "typo". But feel free to change it.

    Not sure if its a “typo”. But feel free to change it.

12. • CommentRowNumber12.
    • CommentAuthorTim_Porter
    • CommentTimeSep 21st 2012
    • PermaLink
    Author: Tim_Porter
    Format: MarkdownItexI noticed that in the letter to Faltings AG uses $\pi_1(X,\xi)$ and states that $\xi$ is a geometric point, so I think it is just a slip.

    I noticed that in the letter to Faltings AG uses $\pi_1(X,\xi)$ and states that $\xi$ is a geometric point, so I think it is just a slip.

13. • CommentRowNumber13.
    • CommentAuthorzskoda
    • CommentTimeSep 24th 2012
    • PermaLink
    Author: zskoda
    Format: MarkdownItexI added the reference of foundational type having a sample section on [[anabelian geometry]]. It is in Russian * [[Nikolai Durov|N. V. Durov]], _Топологические реализации алгебраических многообразий (Topological realizations of algebraic varieties)_, preprint POMI 13/2012 (in Russian) [abstract](http://www.pdmi.ras.ru/preprint/2012/12-13.html), [pdf.gz](ftp://ftp.pdmi.ras.ru/pub/publicat/preprint/2012/13-12_rus.pdf.gz) > ABSTRACT: This work is dedicated to the study of different realizations of algebraic varieties inside topological categories, e.g., the categories of topological spaces or $\infty$-topoi. Such realizations might be used in principle to reduce problems from algebraic geometry or number theory, such as the search for rational points on a variety, to topological problems. > Various abstract properties of such realizations are studied, and concrete examples are discussed. Relation to anabelian geometry and ``three-dimensional model'' of ${\operatorname{Spec}}{\mathbb Z}$, as well as Morel--Voevodsky motivic homotopy types, is mentioned. > Key words: algebraic varieties, realization, motives, motivic homotopy types, Morel--Voevodsky construction, etale topology, higher topoi, higher categories, anabelian geometry, three-dimensional model

    I added the reference of foundational type having a sample section on anabelian geometry. It is in Russian

    • N. V. Durov, Топологические реализации алгебраических многообразий (Topological realizations of algebraic varieties), preprint POMI 13/2012 (in Russian) abstract, pdf.gz

    ABSTRACT: This work is dedicated to the study of different realizations of algebraic varieties inside topological categories, e.g., the categories of topological spaces or $\infty$-topoi. Such realizations might be used in principle to reduce problems from algebraic geometry or number theory, such as the search for rational points on a variety, to topological problems.

    Various abstract properties of such realizations are studied, and concrete examples are discussed. Relation to anabelian geometry and “three-dimensional model” of , as well as Morel–Voevodsky motivic homotopy types, is mentioned.

    Key words: algebraic varieties, realization, motives, motivic homotopy types, Morel–Voevodsky construction, etale topology, higher topoi, higher categories, anabelian geometry, three-dimensional model

14. • CommentRowNumber14.
    • CommentAuthorTim_Porter
    • CommentTimeSep 24th 2012
    • PermaLink
    Author: Tim_Porter
    Format: MarkdownItexI have created an entry on [[Grothendieck's section conjecture]] and linked it to several new people entries, plus the 'homotopical' blog entry by Andreas Holmstrom, October 4, 2009.

    I have created an entry on Grothendieck’s section conjecture and linked it to several new people entries, plus the ’homotopical’ blog entry by Andreas Holmstrom, October 4, 2009.

15. • CommentRowNumber15.
    • CommentAuthorzskoda
    • CommentTimeSep 25th 2012
    • PermaLink
    Author: zskoda
    Format: MarkdownItexMaybe redirect section conjecture would make sense. I heard it referred just as that. Is there another section conjecture which would make this ambiguous ?

    Maybe redirect section conjecture would make sense. I heard it referred just as that. Is there another section conjecture which would make this ambiguous ?

16. • CommentRowNumber16.
    • CommentAuthorTim_Porter
    • CommentTimeSep 25th 2012
    • (edited Sep 25th 2012)
    • PermaLink
    Author: Tim_Porter
    Format: MarkdownItexYou mean rename as [[section conjecture]]. That seems alright. I will go ahead and do that. I have seen it called the anabelian section conjecture, but as it does not limit itself to just anabelian varieties that seems not so good as a name.

    You mean rename as section conjecture. That seems alright. I will go ahead and do that.

    I have seen it called the anabelian section conjecture, but as it does not limit itself to just anabelian varieties that seems not so good as a name.

17. • CommentRowNumber17.
    • CommentAuthorzskoda
    • CommentTimeSep 25th 2012
    • (edited Sep 25th 2012)
    • PermaLink
    Author: zskoda
    Format: MarkdownItexThanks, I also put a redirect [[anabelian section conjecture]] which works along with [[section conjecture]] and [[Grothendieck's section conjecture]] (the latter however has a cache bug problem in the moment).

    Thanks, I also put a redirect anabelian section conjecture which works along with section conjecture and Grothendieck’s section conjecture (the latter however has a cache bug problem in the moment).

18. • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeJul 12th 2014
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded a [pointer](http://ncatlab.org/nlab/show/anabelian+geometry#Tschinkel14) to * [[Yuri Tschinkel]], _Introduction to anabelian geometry_, talk at _[Symmetries and correspondences in number theory, geometry, algebra, physics: intra-disciplinary trends](https://www.maths.nottingham.ac.uk/personal/ibf/files/sc3.html)_, Oxford 2014 ([slides pdf](http://www.cims.nyu.edu/~tschinke/.talks/oxford14/oxford14.pdf))

    added a pointer to

    • Yuri Tschinkel, Introduction to anabelian geometry, talk at Symmetries and correspondences in number theory, geometry, algebra, physics: intra-disciplinary trends, Oxford 2014 (slides pdf)
19. • CommentRowNumber19.
    • CommentAuthorTim_Porter
    • CommentTimeMay 31st 2018
    • (edited May 31st 2018)
    • PermaLink
    Author: Tim_Porter
    Format: MarkdownItexSomeone (alex) has removed a quote from [[anabelian geometry]]. It is not clear why and they have not flagged it up here. The same person had changed something in that paragraph a few days ago. There may be a good reason for that change but that is not clear.

    Someone (alex) has removed a quote from anabelian geometry. It is not clear why and they have not flagged it up here. The same person had changed something in that paragraph a few days ago. There may be a good reason for that change but that is not clear.

20. • CommentRowNumber20.
    • CommentAuthorTim_Porter
    • CommentTimeMay 31st 2018
    • PermaLink
    Author: Tim_Porter
    Format: MarkdownItexNote we have two pages in the Forum on this entry. This is with Anabelian the other with anabelian. Can they be merged somehow?

    Note we have two pages in the Forum on this entry. This is with Anabelian the other with anabelian. Can they be merged somehow?