Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
created formal disk with some default text, just so that the links from function field analogy – table point to something
the entry p-adic number had (and has) its Definition-section filled with a lengthy recollection of the p-adic integers. I have split into two subsections, such as to make it more clear where the actual definition begins.
created a minimum at Tate’s acyclicity theorem. Also created a minimum at Banach module.
in non-archimedean analytic geometry there is a standard concept of quasi-net used notably in the definition of Berkovich analytic spaces.
I have created a minumum entry on this, in the course of creating a bunch of non-archimedean analytic entries. But clearly this needs some comment on terminology. Help is welcome.
started real space
(of course that may eventually want to be disambiguated, but maybe for the moment it’s okay)
I worked a bit on bringing the list of structures present in a cohesive (oo,1)-topos into shape, expanding it and filling in details. See the table of contents at cohesive (infinity,1)-topos.
Added some more (basic) information on complex conjugation to complex numbers.
added to moduli space of curves a paragraph mentioning the result by Harer-Zagier on the orbifold Euler characteristic of being .
created some minimum at augmented Teichmüller space.
I have also touched moduli stack of curves and Teichmüller space and Deligne-Mumford compactification adding references and various little pointers etc.
I have touched étale groupoid and various entries related to this.
I have made orbit space redirect to orbit, though eventually it might want to be a separate entry.
Also I have made foliation theory redirect to folitation, though eventually it might want to be a separate entry.
I have added Deligne-Mumford stack as a “related concept” to étale groupoid, though eventually what I am after is a complex of entries that discusses approaches to a general notion of étale ∞-groupoids and how these sub-entries fit into a more general story.
So I’ll be creating a stub étale ∞-groupoid, but I am not sure if I have time and energy to have it be more than a reminder for things to look into later.
started to split off Banach ring from Banach algebra. But need to interrupt now.
started some minimum at Donaldson-Uhlenbeck-Yau theorem
The relation between slope-(semi-)stability of vector bundles and the general concept of (semi-)stability in the sense of geometric invariant theory seems to be a well-kept secret as far as expositions and lecture notes etc. go. One place where I see a genuine review of this relation is
I have created an entry
(with a bunch of variant terms redirecting to it) that is presently just a glorified pointer to the relevant pages in this thesis. Then I have added related comments to the existing entries
might anyone have an electronic copy of the English version of Brylinski-Zucker 91 “An overview of recent advances in Hodge theory”?
have added to normed field the statement that if the product preserves the norm strictly (by equality, not just by inequality) then one speaks of a “valued field”.
I put a complete definition at linear logic.
added to Gromov-Witten theory and to orbifold pointers relating to Ruan et al.’s work on orbifold GW theory
As I’ve added some material to classifying topos of the theory of objects, I’ve done some rewriting as well. Feel free to rectify!
I created the page walking structure. I’m open to better names for it. It also probably needs to be linked from a bunch of different places.
should say that yesterday, right before my battery died, I had started a bare minimum at sheaf of rational functions, just so as to complete the corresponding entry at function field analogy – table
added to real analytic space the statement and reasoning of Whitneys’s theorem (unformatted for the moment, am in a rush)
started a table-for-inclusion
and included it into relevant entries. (But it’s still tiny at the moment.) Also started a bunch of stubs needed for this, such as
Hecke correspondence, Hecke transform, Hecke eigensheaf, electric eigenbrane, magnetic eigenbrane.
Neither of these have much content yet apart from a lightning Idea-section, a pointer to some literature and cross-links.
started some minimum at ’t Hooft operator
put something basic into form of an algebraic group
have added some more references to logarithmic geometry and cross-linked a bit. (but there is still no genuine content)
Created p-local module.
started a minimum at analytification, mainly interested for the moment in collecting the references now given there which discuss analytification of algebraic (etc.) stacks
slightly expanded and prettified a bit at almost complex structure (nothing non-trivial, just cosmetics)
I have expanded just a little at KR-theory by giving it an actual Idea-paragraph and adding some more references.
I gather (via this nice MO comment) that
The functor that takes linear algebraic groups to their -points constitutes an equivalence of categories between compact Lie groups and -aniosotropic reductive algebraic groups over all whose connected components have -points.
For as in this equivalence, then then complex Lie group is the complexification of .
I have a gap in my education here and would like to fill it. What’s a good source that discusses this statement a bit more? And which one of Chevalley’s articles is this result originally due?
started a minimum at p-convex polarization
added to absolute Galois group and to Grothendieck-Teichmüller group brief pointers for the inclusion of the former into the latter (for the case of the rationals) and a pointer to
I noticed tha tthe entry separable closure existed but was effectively devoid of content. I have now copy-and-pasted the relevant paragraphs from the entry Galois theory into it.
Have given Frölicher spectral sequence an Idea-paragraph and some pointers, but it is still a stub.
I created this page: http://ncatlab.org/nlab/show/The+Mathematical+Literature
Am I right that I’m supposed to post about this here at the nForum? How big should an edit be in order to deserve a post here?
And can i link from the nForum to the nLab by doing this? The+Mathematical+Literature
I wrote a bit at heap about the empty heap (and its automorphism group, the empty group, which I put in the headline for maximum shock value).
added pointers to the section on cohomology.
Over on MO (in the comments here) Stefan Wendt kindly reminds me of an old Lab entry I once started on B1-homotopy theory. Have added a reference and hope to be adding more.
started Hodge cycle, but my battery is dying right this moment….
gave Hodge symmetry it’s own brief stand-alone entry
Larusson formulates the Oka principle homotopy-theoretically as: a complex manifold is Oka if for every Stein manifold the canonical map
between the mapping spaces is a weak homotopy equivalence (see here).
It is natural to wonder what this looks like in terms of the cohesion of the -topos over .
If we write , then up to possible technicalities to be checked, it should simply mean
where is the internal hom.
(Something close to this (but not quite the same) is what Lawvere calls the “axiom of continuity” in a cohesive topos.)
If instead we work internally and let be the shape modality, then the above is equivalently
In either case, it is a very natural condition to ask for in general cohesive -toposes. Maybe one should call it the Oka-Larusson property or something…
started analytic geometry – contents to be included as “floating table of contents”, and accordingly included it into relevant entries
I split off an entry applications of (higher) category theory from the entry nPOV.
Hopefully we find the energy to further improve this entry in various ways. For the moment I just added a 1-line intro. And a quote, which I think hits the nail of this entry on the head.
added pointers to Fornaess-Stout on complex polydiscs here
Somebody emailed me highlighting that the text green here, revision 69 of Dold-Kan correspondence does not quite parse.
I didn’t write this,though. There is a definition meant to be equivalent to that at combinatorial spectrum, but at least some indices need renamining, and it seems maybe more needs to be fixed or at least added. Not sure. Also I absolutely don’t have the leisure to look into this right now. I hope somebody finds the energy to look into it.
I’ve created a page on the Artin-Mazur formal group.
created Serre duality with a simple minimum of content
(I have also briefly touched a bunch of related entries on Dolbeault cohomology etc. but most of them are still in a sad state and need work)
we didn’t have any entry defining coherent cohomology, did we?
(I notice that we are lacking also an entry coherent object. That really needs to be created.)
quick stub for morphism of finite type (redirecting also morphism of locally finite type)
Added some new material to linguistics.
gave intersection theory an Idea section. Clearly, there is room for improvement, but it’s a start.
In the course of this I have created at stub for Bézout’s theorem, gave Serre intersection formula an Idea-section (please feel invited to expand further!) and cross-linked all this and a few more entries.
added some minimum of content to the old stub divisor (algebraic geometry)
started polarized algebraic variety
added the definition in complex analytic geometry with a pointer to degree of a coherent sheaf
created exponential exact sequence with the obvious basic comments. Cross-linked with Planck’s constant, with multiplicative group and circle group, and with Kummer sequence.
added to Theta characteristic two further brief Properies-paragarphs: As metaplectic and Spin-structure over (Kähler-)polarized varieties and Over intermediate Jacobians.