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I added a section on Lawvere’s definition to adjoint functor and also made an article for Functorial Semantics of Algebraic Theories.
created some bare minimum at mod p Whitehead theorem
created stub for
with just some references and
with just some pointers, cross-linked with
To be expanded…
I suppose we were lacking an entry on p-localization (?)
I’ve created a page for the Witt vectors. It seems that even with all that I wrote here (don’t worry I had a set of about 10 blog entries I wrote a few months ago that I just condensed, so I didn’t write this whole thing tonight) there are all sorts of things still missing here. The Witt functor is mention at Lambda-ring and there seems to be connections to the field with one element (?!). I just needed to refer to Witt vectors in the next few pages I want to make, so I decided this had to come first. Dieudonne module will need it and obviously Witt cohomology will need it.
added to étale topos some basics in the section Properties – Base change and sheaf cohomology
killed a spam page, now called spam
I felt like starting a table infinitesimal and local - table and included it into the relevant entries. So far it reads as follows:
| first order infinitesimal object | infinitesimal | ⊂ | formal = arbitrary order infinitesimal | ⊂ | local = stalkwise | ⊂ | finite |
|---|---|---|---|---|---|---|---|
| derivative | Taylor series | germ | function | ||||
| tangent vector | jet | germ of curve | curve | ||||
| Lie algebra | formal group | local Lie group | Lie group | ||||
| Poisson manifold | formal deformation quantization | local strict deformation quantization | strict deformation quantization |
Can be further expanded, clearly.
The entry Borel-Weil theorem mentions extensions of the theorem to quantum groups, without however giving a reference. I just got an email asking for these.
The statement dates from August 19, 2009, due to Zoran.
created a bare minimum at branched cover of Riemann sphere, just to record the fact that every compact connected Riemann surface admits this structure.
I began adding proofs of Lemma 1-4 to the page transfinite construction of free algebras. The layout of the two array environment has to be fixed; proof of 3-4 to be added.
Any help/suggestion is extremely appreciated!
gave p-adic complex numbers an entry
Someone (anonymous) has created an empty page oon finite dimensional vector spaces.
created a minimum at global field
needed to point to restricted product, so I created a bare (and unsophisticated) minimum
I mostly wanted to record the correct meaning of this term. Then maybe later I can use this as a reference to fix Wikipedia (^_^). But there's a bit more here too.
gave Cartesian space a TOC and added some statements and references.
Edited biholomorphic function to follow the same format as diffeomorphism. In particular, this means that I qualified biholomorphic function to refer only to maps between complex manifolds. Is there a more general definition of holomorphic functions between complex analytic spaces?
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 ℳg,1 being ζ(1−2g).
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 G to their ℝ-points G(ℝ) constitutes an equivalence of categories between compact Lie groups and ℝ-aniosotropic reductive algebraic groups over ℝ all whose connected components have ℝ-points.
For G as in this equivalence, then then complex Lie group G(ℂ) is the complexification of G(ℝ).
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 nLab 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….