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Research Diary Log. Brahim Marzouk. Maths Research Diary. Research diary log. ------------------- Author : Marzouk Brahim. url : http://bmarzouk.free.fr/search.txt Created : 21.09.20. Last update : 04.08.21. About ~ 9700 lines, 300p. Diary : BEGIN @ ~ Line 450. p10. Some symbols : * = videos reports (mostly youtube math videos). ® = reading reports (articles, books, web pages). • = Personal notes; often enclosed between (thick or thin) arrows; thick being for important remarks, the thinner are more for comments. "===>" or "--->" mark their begining and the reverse ones, "<===" or "<---" mark their end. © = computers notes. Abbreviations & jargon : I) maths. ab = abelian(nisation). alg = algebra(ic) or algebraically. algeo = algebraic geometry. app = application. approx = approximate (tion). bbki = Bourbaki. 1 of 362 Brahim Marzouk. Maths Research Diary. dbl = double. dbt = doubt(ful). crt = criterion. geom = geometry. diag = diagram, diagonal, diagonalisable. dioph = diophantine. def = definite, definition(s). der = derived, derivative, derivation. rep = representation. den = denominator. hom = homomorphi(c/sm), homeomorphi(c/sm). irr = irreducible. lin = linear, linearity. num = numerator. prg = program. ref = reference. reg = regular. res = resolution, resultant, result. diff = differentia-te/ble/l. top = topolog-y/ical. frac = fraction-al. dep = dependent, dependency. det = determinant. endo = endomorphism, endofunctor, endogenesis. ext = extension, extended, exterior. func = function, functor. cj(s) = conjecture(s). rh, RH = Riemann Hypothesis. bsd,BSD = Birch-SwinnertonDyer conjecture. cplx = complex. thm = theorem. ppties = properties. grp(s) = group(s). th = theory. nb = number. rat = rational. 2 of 362 Brahim Marzouk. Maths Research Diary. sing = singular/ity/ities. transc = transcendent(al). tr = transcendent(al). var = variety, variable. vect = vector, vectorial. k_ = algebraic closure of k. II) computer sciences. asm = assembly. bt = bluetooth. conf = config(uration). ctrl = control. deb = Debian. dwload = download, pull. ecc = elliptic curve cryptography. gui = graphical user interface. prg = program. repo = repository. hd = hard-drive. ide = integrated developpement environement. box = computer system (laptop, desktop pc). e = electronics. src = source. phone = smartphone. vid(s) = video(s). rm = remove, delete. dev = development, device. os = operating system. vm = virtual machine. ffox = Firefox. g = Google. ytube = YouTube. wkp = Wikipedia. 3 of 362 Brahim Marzouk. Maths Research Diary. evn = Evernote. m$ = Micro$oft. win$ = Window$. insta = Instagram. fb = facebook. To Do. ====== • Coquilles in txts and TeXtes. ------------------------------- 0) search.txt : separate lines : date-begin. alternating sum. riemann hurwitz. modulo Q_ algebraic equivalence. Spreading out sets the dna of the forecoming collected data. Bouquets : spreading out- nodes along Spec(Z) Arizona. Log Div, Log Der. th endo. Sites "huh?" in pc. add link in blogspot.com About. x. post a winter tips page. 1) serie.tex : max (ultra metric). check base solution. -> Change ugrad series templates, retrieve underlines. 4 of 362 Brahim Marzouk. Maths Research Diary. p1. replace "l-adique" by algèbre polynomiale graduée de degré ∞ = limite projective pour d -> ∞ d'algèbres graduées Ad[X], de polynomes de degré <= d. p4 : -1 in numerators of F(z) (rational function+closed form). p4 : bibliography "Fourier". 2) critere.tex p1. "sneaky" with "intricate". "former" by "former algebraic". p2. "path" with "band". p2. "Another object" with "Another object which is original". p5. "In that formulation, only an algebraic version". p5. "is not possible as formulated here". "No non- trivial". p6. "References" with "Reference." --> For corrections/updates, use different : a) fonts. b) fonts styles. c) colors. 3) mem.tex. Groupe galois. Dependence π et E(√2/2). r et π algebriquement independents. p2 bot : La question de la répartition. 5 of 362 Brahim Marzouk. Maths Research Diary. p5 mid : sur une variété algébrique. p5 bot : spécialisation locales. p8 bot : localisés du corps des fonctions. p11 bot : variétés; indep algebriques de nombres (reels) p14 mid : cj famille algebriquement libre sur Q alors ... pas de Q-pt non trivial. p22 top : G_F(V)=h_F(G_V); l'ideal serait que h_F = F; ie G_F(V)= F(G_V). p22 bot : Du coté des motifs, déjà leurs applications aux points précédents ( approximations des periodes fondamentales; Hodge De Rham); puis considerer K=k(P(V)) avec k = Q_ ... p22 bottom : en termes d'invariants periodiques. 4) slides.tex The left versions of 2007 has many. I remember that last updated versions of 2009 (in Hitachi stuck-hd) were bettered with corrections. ===> Try to fix that hd : a) find parts or a complete spare. b) learn technics. • Rewrite. ---------- • DNDE α(β+½(γ-β)) α+d[(0,γ); (α,β)]=α+√(α²+(γ-β)²) 6 of 362 Brahim Marzouk. Maths Research Diary. • Glueing C/6 +L(ramble). Seems ok. Q-pt → (λ,μ,ρ) alg dep, since (λ,μ) are already alg dep (nested degeneration case). • Transcendental cos. eit =cos t + isin t, would be algebraic. (it, eit) both alg. But z alg => ln z transc (Lindemann Baker th) : contradiction, if z=eit. So if t rat≠0, cos t transc. Compute k^. • Motives. $V, measure Μodule V. $Alg→transc. Polyakov measure. • Surface. T=tore(r,R) V(T) =2rS(T). X(T)=0. π1(T)=Z®Z • Exp. xy=exp(x-y). • Ebauches. 1) Bouquets d'espaces. 7 of 362 Brahim Marzouk. Maths Research Diary. Y--Y--Yi--Y--Y. (Yi,fi) "arrows above X" : \ |fi | | / fi : Yi --> X applications. X. If X is a topological space covered by a family of sets ¥=(Yi) Topology on ¥ or the (Yi) : final topology associated to the (fi). When (fi) are etale morphisms from a fixed Y (so both X and Y are schemes), this gives the etale topology on Y. Etale morphism Y --f--> X. Existence of a covering (Uα) of X such that Vα=f-¹(Uα) is a covering of Y satisfying fα=f|Vα : Vα ---~--> {α}xUα and other regularity-flatness ppties. Existence of a covering (Ui) of Y such that f|Ui : Ui--fi-->f(Ui) gives a covering (f(Ui)) of X with f(Ui) ~ {i}xUi; plus other prerequisites of regularity-flatness. ==> Consider the 2nd level : bouquets above the nodes of that structure or even bouquets above the structure itself; or add some structure to ¥ for instance : 2) Bouquets de torseurs. Y--Y--Yi--Y--Y. ¥ = (Yi) : (X-)torsors under the action of Gi .πiهfi| | / fi = Fi | \ 8 of 362 Brahim Marzouk. Maths Research Diary. X. (Yi,Gi,fi) family of torsors above X, under the actions of the groups (Gi). If the (Yi) are a fixed Y; a family of groups (Gi) acting on Y, invariantly against a fixed morphism to X, gives rise to a family of torsors above X. If the family (Gi) is replaced by a family of families (((Gij)j)i) we get a double-indexed family of torsors. Clarify : a) The isomorphism classes of such families are given by the cohomology classes G-structure of |H1(X,G) where |H(X,G)=H(G, Hb(X)). b) The isomorphism-classes of such families are given by the cohomology classes living in |H1(X,G)." "Define |H(X,G)=H(G,Hb(X)". c) Explicit order in H. H(X, Λ)= H(π¹(X,x), Λ) for any constant abelian sheaf Λ. * Tropical geometry. Moduli (parametrized curves) : from combinatorial intersections ppties at degenerating values of the parameter, ie that give "degenerate cases", trying to pull back those data for the whole moduli from those simpler "degenerate" situations. Framework : on discrete valuations fields, aka non archimedean ones. A=C((t)): Laurent power series. C((t))_ = Frac(A)_ = C((t^¹/n)) Puiseux series. 9 of 362 Brahim Marzouk. Maths Research Diary. LINKS ===== ® Forum. https://math.stackexchange.com/ https://mathoverflow.net/ https://mathoverflow.net/questions/127633/what-are-the- possible-motivic-galois-groups-over-mathbb-q https://ncatlab.org https://ncatlab.org/nlab/show/period ® Seminars. http://m.mathnet.ru/php/seminars.phtml?wshow=comsoon& option_lang=eng https://researchseminars.org/seminar/NTWebSeminar Sigma forums Cambridge. ® Library. edx.org numdam.org projecteuclid.org https://press.princeton.edu/books/paperback/9780691193779 /arithmetic-and-geometry https://pi.math.cornell.edu/~kbrown/publications.html 10 of 362 Brahim Marzouk. Maths Research Diary. ® Bookshelves. http://www-fourier.ujf-grenoble.fr/~marin/une_autre_crypto /Livres/ http://nozdr.ru/biblio/kolxoz/m/ma https://zh.b-ok.africa/book/2710292/3ed31a http://www.ebyte.it/library/refs/Refs_Math_Books.html http://www.bdim.eu/item?id=BUMI_2009_9_2_1_259_0 https://archive.org/download /MathematicsEbooksMegaCollection https://epdf.pub/number-theory-04-transcendental- numbers.html ® Encyclopedias. https://encyclopediaofmath.org https://encyclopediaofmath.org/wiki/Gel%27fond- Schneider_method https://planetmath.org/ https://planetmath.org/PrimeSpectrum ® Scholars articles. Joseph Ayoub http://user.math.uzh.ch/ayoub/ 11 of 362 Brahim Marzouk. Maths Research Diary. Annette Huber https://home.mathematik.uni-freiburg.de/arithgeom/ Giesbert Wustholtz https://scholar.google.com/citations?user=9knV80QAAAAJ& hl=en https://scholar.google.fr/scholar?start=10& q=wustholz+elliptic+and+abelian+period+spaces&hl=en& as_sdt=0,5&as_vis=1 New researcher Martin Orr http://www.martinorr.name/blog/2015/10/06/periods-of- abelian-varieties/ ® Vulgarisation. http://images.math.cnrs.fr/Le-rang-des-courbes- elliptiques.html http://eljjdx.canalblog.com ® Docs. https://docs.google.com/document /d/1EMhjvhtcQmXvBhaFeQo7f_Rg7O32y0e1M0tUEFilsxY /edit?usp=sharing File conversion https://www.print-driver-fr.com/howto /convertir_djvu_to_pdf.html UTF8 (extensions) ==== 12 of 362 Brahim Marzouk. Maths Research Diary. a) Symbols. ¹ ½ ⅓ ¼ ⅛ ² ⅔ ³ ⅜ ¾ ⁴ ⅝ ⅞ ⁿ ∅ ⊗ ⊕ ∮ ∫∂ ↩ → ∀ × φ ∈ Ц ∏ √ ∑ π ϕ φ ∈ ‰ % _ — – · . ≤ ‹ « ≥ › » ↑ ↓ ← → ′ ″ ≠ ∞ ≈ { } ∆ § ¶ × ÷ π Π √ • | ` ~ © ® ™ ℅ « » ” “ „ : ¡ ¿ , _ / … _ ₱ ¢ £ ¥ ¢ ★ † ‡ ¡ ¿ > ± ♪ ♥ ♦ ♣ ♠ b) Accents. à á â ä æ ã å ā é è ē ê ë ì í ì ï ī û ú ū ü ù À Á Â Ä Æ Ã Å Ā É È Ē Ê Ë Û Ú Ū Ü Ù Û Ú Œ Ó Ô Ö Ò Ø Ō Õ c) Greek. α β γ δ η ς ε ρ τ υ θ ι ο π α σ δ φ γ η ξ κ λ ζ χ ψ ω β ν μ Α Σ Δ Φ Γ Η Ξ Κ Λ Ε ς Ρ Τ Υ Θ Ι Ο Π Ζ Χ Ψ Ω Β Ν Μ d) Russian.
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