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    • Page created, but author did not leave any comments.

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • brief category:people-entry for hyperlinking references

      v1, current

    • Created an article, modeled on Borel set

      v1, current

    • started an entry F-theory (the string-theoretic notion)

    • brief category:people-entry for hyperlinking references

      v1, current

    • am creating this entry just for ease of hyperlinking, since in many entries I find myself writing “real cohomology, i.e. …, as computed by …”, and all this should just be dealt with in a dedicated entry.

      v1, current

    • Page created, but author did not leave any comments.

      v1, current

    • stub for tachyon, but out of time now

    • Page created, but author did not leave any comments.

      v1, current

    • Added quadrability of a cospan (and coquadrability of a span) as well as quadrability/coquadrability of a category C. The word "quadrable" means "squarable", but "squarable" isn't a real word. The word "quadrable" is the proper translation of the French "carrable".

      Note that while the translation "quadrable" is uncommon, the term "carrable" in French is standard.

    • added pointer to

      • Hermann Minkowski, Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern, Math. Ann. (1910) 68: 472, reprinted from: Nachrichten der Kgl. Ges. d. Wiss. zu Göttingen, Math.-phys. Kl., Sitzung vom 21. Dezember 1907 (doi:10.1007/BF01455871)

      diff, v13, current

    • I have created an entry spectral symmetric algebra with some basics, and with pointers to Strickland-Turner’s Hopf ring spectra and Charles Rezk’s power operations.

      In particular I have added amplification that even the case that comes out fairly trivial in ordinary algebra, namely Sym RRSym_R R is interesting here in stable homotopy theory, and similarly Sym R(Σ nR)Sym_R (\Sigma^n R).

      I am wondering about the following:

      In view of the discussion at spectral super scheme, then for RR an even periodic ring spectrum, the superpoint over RR has to be

      R 0|1=Spec(Sym RΣR)Spec(R(nBΣ(n) n) +). R^{0 \vert 1} \;=\; Spec(Sym_R \Sigma R) \simeq Spec\left( R \wedge \left( \underset{n \in \mathbb{N}}{\coprod} B\Sigma(n)^{\mathbb{R}^n} \right)_+ \right) \,.

      This of course is just the base change/extension of scalars under Spec of the “absolute superpoint”

      𝕊 0|1Spec(Sym 𝕊(Σ𝕊)) \mathbb{S}^{0\vert 1} \simeq Spec(Sym_{\mathbb{S}} (\Sigma \mathbb{S}))

      (which might deserve this notation even though the sphere spectrum is of course not even periodic).

      This looks like a plausible answer to the quest that David C. and myself were on in another thread, to find a plausible candidate in spectral geometry of the ordinary superpoint 0|1\mathbb{R}^{0 \vert 1}, regarded as the base of the brane bouquet.

    • Expanded motivation section and wrote a bit on coordinate representation.

      diff, v5, current

    • added a sentence to this otherwise empty entry. But it remains a stub

      diff, v2, current

    • Over in another thread, David Roberts asks for explanation of a bunch of terms in QFT (here).

      In further reaction I have started a minimum of explanation for one more item in the list: split supersymmetry.

    • a stub, to record some references

      v1, current

    • some minimum, in order to give a home to today’s

      • Dong-Yang Wang, Ya-Dong Yang, Xing-Bo Yuan, bcτν¯b \to c \tau \bar \nu decays in supersymmetry with R-parity violation (arXiv:1905.08784)

      v1, current

    • Page created, but author did not leave any comments.

      v1, current

    • some minimum, for completeness and to record references

      v1, current

    • Finally added to fracture theorem the basic statement of the “arithmetic fracture square”, hence the following discussion.


      The number theoretic statement is the following:

      +– {: .num_prop #ArithmeticFractureSquare}

      Proposition

      The integers \mathbb{Z} are the fiber product of all the p-adic integers pprime p\underset{p\;prime}{\prod} \mathbb{Z}_p with the rational numbers \mathbb{Q} over the rationalization of the former, hence there is a pullback diagram in CRing of the form

      pprime p pprime p. \array{ && \mathbb{Q} \\ & \swarrow && \nwarrow \\ \mathbb{Q}\otimes_{\mathbb{Z}}\underset{p\;prime}{\prod} \mathbb{Z}_p && && \mathbb{Z} \\ & \nwarrow && \swarrow \\ && \underset{p\;prime}{\prod} \mathbb{Z}_p } \,.

      Equivalently this is the fiber product of the rationals with the integral adeles 𝔸 \mathbb{A}_{\mathbb{Z}} over the ring of adeles 𝔸 \mathbb{A}_{\mathbb{Q}}

      𝔸 𝔸 . \array{ && \mathbb{Q} \\ & \swarrow && \nwarrow \\ \mathbb{A}_{\mathbb{Q}} && && \mathbb{Z} \\ & \nwarrow && \swarrow \\ && \mathbb{A}_{\mathbb{Z}} } \,.

      =–

      In the context of a modern account of categorical homotopy theory this appears for instance as (Riehl 14, lemma 14.4.2).

      +– {: .num_remark}

      Remark

      Under the function field analogy we may think of

      • Spec()Spec(\mathbb{Z}) as an arithmetic curve over F1;

      • 𝔸 \mathbb{A}_{\mathbb{Z}} as the ring of functions on the formal disks around all the points in this curve;

      • \mathbb{Q} as the ring of functions on the complement of a finite number of points in the curve;

      • 𝔸 \mathbb{A}_{\mathbb{Q}} is the ring of functions on punctured formal disks around all points, at most finitely many of which do not extend to the unpunctured disk.

      Under this analogy the arithmetic fracture square of prop. \ref{ArithmeticFractureSquare} says that the curve Spec()Spec(\mathbb{Z}) has a cover whose patches are the complement of the curve by some points, and the formal disks around these points.

      This kind of cover plays a central role in number theory, see for instance thr following discussions:

      =–

    • Stub about blockchain platform EOS known for high performance.

      v1, current

    • I got tired of having to fight my way through Kelly’s monster yet again, and created transfinite construction of free algebras. I couldn’t really think of a good name for this page; suggestions are welcome.

    • Page created, but author did not leave any comments.

      v1, current

    • a minimum, for the moment just so as to record some references on Pin(2)Pin(2)-equivariant homotopy theory (as kindly pointed out by David Roberts)

      v1, current

    • I have spent some minutes starting to put some actual expository content into the Idea-section on higher gauge theory. Needs to be much expanded, still, but that’s it for the moment.

    • Added (not very elegantly) the relation to Meyer-Vietoris sequence at Dold-Thom theorem.

    • started gauged WZW model, but no content yet, am just recording some references…

    • What is a weakly separated space ?

      Anonymous

      v1, current

    • This is my first hook to the n-lab, I am pretty sure that isomorphism is an overly strong condition, and that any is a too weak restriction.

      Please see the wikipedia article on the principle of bivalence. https://en.wikipedia.org/wiki/Principle_of_bivalence

      I am unsure as how to proceeed.

      vukovinski

      diff, v4, current

    • Page created, but author did not leave any comments.

      vukovinski

      v1, current

    • Page created, but author did not leave any comments.

      Anonymous

      v1, current

    • starting something, but I am running out of steam now

      v1, current