From 5ffddfe108b17f79124b27bb6c7957d5d7a8a66b Mon Sep 17 00:00:00 2001 From: Sixto Date: Wed, 28 May 2025 01:10:18 +0200 Subject: [PATCH] =?UTF-8?q?A=C3=B1adida=20la=20bibliograf=C3=ADa=20inicial?= =?UTF-8?q?=20aunque=20todav=C3=ADa=20sin=20referencias=20dentro=20del=20t?= =?UTF-8?q?exto.?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- TFG_Sixto_José_Martínez_Gan.pdf | Bin 234798 -> 271721 bytes TFG_Sixto_José_Martínez_Gan.tex | 10 +++++ bibliografia.bib | 64 ++++++++++++++++++++++++++++++++ 3 files changed, 74 insertions(+) create mode 100644 bibliografia.bib diff --git a/TFG_Sixto_José_Martínez_Gan.pdf b/TFG_Sixto_José_Martínez_Gan.pdf index 8b9eb780070b7836a90a73339955e30f49acb33c..c09d067b668b02bf90457f4d2386c9fed83ab686 100644 GIT binary patch delta 100607 zcmZs>Q*fYN&@CL>wr$&-*tRjT{lvCy+qRR5GqIhCCz)9P`+eu)uR3*ZcCG5JuDdZZf}NL#HKjNeOaU`6rv|rCwWH{1}Y@KR7JlSuF>=Ez!eQsm~zZ_vpW|gRd0Y28{o4KUF z8hyp6k3Ds}4dtR;hGdtYV@?^xN`GEHF`l%tgQpN236Q{%4f3FX&dZGwLL0Sixzb_H zmJ=g{A-|7fFkNrk`>%2LJkPe*0et*NMV#{n11|m%eT=O&<+?rj;*MGDA2-zs%hy*V zYiBs&=h@f1mN9TJHm5CR7A`W%iZV&2X-kmGK5KMc^lz!!s|O>yn)*!KvRpNv-Q2|a zBjPCR)Lw{Z5QP77F)T7uXc6B%K@pq1O#Vf)K9|YD{wl*6d&5FK+=N_;0Ez=)H!QP> z;XbZ*m%#AfnoVPrltUGP!pFoY+syKc#u#my ztZDDK9ob^CAe(zLy2!x9Cb`nhpsdf*X%|Tvrb?c2`sU{PC5_l^Z>y0v_Zl82l#CwXe=9&P!K|?F&SVW*GMHHepj&XXTfl9?qAYlGRxfxrBrr zO2J$PZDDY7db8kWo0(P_P~n>Ko>)i?HJ~pucxD9ZwA9r?iox> z?QX9BH~6&X-QS;?NNE;NEe_p5-;lKhWO`N&^M;ZXvWd9ZjUXl#JEFlM${M}dl%V>F zJzbfUqBQHZz26dv$U9=-jgyFzr(jo0Mqm2OfREoRw%0!hprIA~)Dn?QJ0z|Q!xYRA zrxAoW8~ObSOF1rTTG@o(&nXpzW4*dtmotx1OMJ(zrYghmU4)B^=;a^T0i6x(O@i4G zgZFW+H%^#2EnC9|0~Dyhl*=gjT_T>rF$|`SG+{zq=xya^)1t{bTO5((u0T}AAb(0z z#A5O|b6}_gAX@!ydp#rrqN=g;M7V!{;c(j+>Q0dc^A-9PBm>(%7?1*p6zaa^Y=eU- zJ9DE?Y>)JvId2QH-1)|0yW*miBJa~iAK|L17&EJG*5lQ|6CTlM?Z^LUVwpnrdn7wc z%&D&Ux!iiwL;So`&)v2OKKS525cJ(1Ju!63;rDS4sKNKxFm*l&-C1_wWV1S|)<)=v zEsFUa>#Sejeo}=wf+(kTBKQqkz>VPfp?5-r$6G_c zX^ari{M3rX>yi~PU%k<(qa_`*DFq!C!XLvn! zm!C*0vfTS8g#m#^Tv8*20;w>y+?O$depF2hNc5_Fa#TUywM$qr*IVp3`T%yv{OtSY z7QFm!mIQIcqLA?0zk3f*m`MKu zf(|^|xJbf7P884RTdBmu7IVkv-$HYhO&Ir?6&9fce_J7v^B2=*d9>kJq^ZtFfAO?# z==4C|Dw@d8JLT2zIOXLpj(bEIu!W@k#k6*YpW>;JpY3-IC{&5uO5S|IXqqZ-l!;p~ zHNbrsubq(*6?^F4^i*7)>NE*9t88!r48R=n+n1C=uyZ(AXg>3{mV<_(R9+nN=BU)m z8s=UtI23N!HuYLFk((D=WmqEbQ$QLliv{wQnAxzqPN?VkqJ<#ndUYChKKZ>$Cwnz0+yCYr8DAxbd7uSB_s>zniGd8AgTxV1Dt6 z;2>7r?cbv87mu**xeyyGJG-ctA){&hS*)B^impaR8+={V=pKc*cdkOgGQVj>NdGhm z7pER2M_P)ad4l?NhJ5xbBQ$a25mHE|QJBj1ee`k6O44LSdp8a9(0XA#AqmZVaF~+= zU-!JCu248o&PY`sgk!8|AYWJk(CXnrBcy0QaE4dU{Gt=vB;VXR?-V5ajRd!2@F+T} zBxOPd2NUx_6p1Ex3T@WrSvuvIt$|N@V0*OE?9}3LdBJ2}v5mlJ=81wx{1QSgZ3bD? zWqe~jQ+@a+VfIu?22(CCAg1Rzgm;~nxa45qUzWF;jUXMEZbG%O1C((c5QN{hW@qTI z65ytG`(|IG>a5Y$EU3vicrtXtQ9Yh_$Io}#)uszAHqd$&3aX$DaBsz~Ynkzj51A=PjcL z5#cAXZw7UM+p}{h<~GMcGkTP~Gs59l5dXV~$Lb9XX-3Lo&R_=tz&>3@xEM5Mr$jQD zXmML0kIjYPr-?L@Q03kJ?!{j9dzu2V)4@OicXCrUxdC-TYC_WYJeqqfG&T713Ck*# z(a%27d{=e7ZNOfiptLk8Ie1T(zz8=bHJ9VSbU=09nSr5pyksX>HM7{5>7kSyMQ@## z1amTK1*&$euk&XHU?7{GS$(Jd87Xv(S3K|w4~@6HM9T3gE@iyEYlBOCx$CEkMG`qi zp8IX}wQ*8RTR^#I4MOimgQtC<>39iy%#QwuZHGP3#(fzWVzQ=G$sFZJ@|FsT%z7jq zw6TRjh+gO?Bi0;(U67MIK~BI1_YoD6R}^u0*9wC-PYzcIRM?9PE6y=#2ezb`J^zxr z#jGc`c9}4H3)1b&{2H_s9EFmE!_Q@N7bs|`W|U(#$lG!>QzxLaoMR%=QwoX{I*;_& zPcJ2j*=lz{pjvw|t7MYzi|4=Nz_y2PZG3#X;Yq#lZ~JO=r(3;E9g3K*AFZt5H|x=~d&TGEY_v{){UQYKEN!1}8U>EZPkUP1oGGyc^s8@LP@w z|CB8ecYoJ}qKBXK?O_%HsECI^E{=mXKkINUqItYU&|-qZ&dALy58y$Q_lx>=FX20| zHNyy+EiecNHQ23K{F+Boy7G>2=t)rZX)FtS$`8=RQ5Q zY%PR=*^5R7*VveEvZGmJo=h1u*i0r`A&YMb)VQYv^|X5>SunWt>SqOhJ3H20Ay(*% zGK#-r4PEPlzwWK=2GyLDkFmLD+dC-Hw+qcjOlq!r>)Xqh@CtS@?Bvt>4Cv3ex@IOc z9_H}qdwjjqSt*A`BT!;sKrw@{w^HgFy2wT0$}N-L{l{;+((kL^<0s)F_;z zO?Ak(gMW^;XB+Pi4uiXb>ycMUDvOK(@JW7695t7t_kYy$&jy_s{WWXvTs&?v#AHqS z1nyv7XqtYy%Ws9JlSL4q%qkb~r@OcARMzuW(>l24h^3>TE0DiDY|K8c7!~LrUimaKyIU9n>eT0; 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zm2<$Nq4#e?>@gwP4h%hWI*)Lyv|uhm1|ed@`EG^XUP4x(l>=PFI89fAwc0|O&y0$P zn?NzOAqq)(N-j`(`oWG^7ddg5>RY5YK+jfOl@0Gd!QO)ozbtu>lITaoG5mfZGL zU&9PbVh=j9M~NHgFh?N*0DWgZBUA9}fly(DD-{C3zjMr$YV8JkX!?n9UcTWydqduO deGt5&j!~ovl7ZsEvaqnTvOtrOi7ALf{|~d`n&toi diff --git a/TFG_Sixto_José_Martínez_Gan.tex b/TFG_Sixto_José_Martínez_Gan.tex index b550ffb..5f367b7 100644 --- a/TFG_Sixto_José_Martínez_Gan.tex +++ b/TFG_Sixto_José_Martínez_Gan.tex @@ -45,6 +45,10 @@ \usepackage{nolbreaks} \usepackage{nicefrac} +% Bibliografía. +\usepackage[backend=biber]{biblatex} +\addbibresource{bibliografia.bib} + \usepackage{algpseudocodex} \algrenewcommand\algorithmicwhile{\textbf{mientras}} \algrenewcommand\algorithmicrepeat{\textbf{repite}} @@ -361,6 +365,8 @@ urlcolor=black]{hyperref} \todo[inline]{Poner ejemplo de un módulo no reflexivo.} \end{ejemplo} + Una discusión más profunda acerca de los módulos reflexivos y sus propiedades puede encontrarse en \cite[\href{https://stacks.math.columbia.edu/tag/0AUY}{Tag 0AUY}]{STACKS}. + En ocasiones, encadenaremos homomorfismos y podemos necesitar expresar las relaciones entre las imágenes y los núcleos de las distintas aplicaciones. Para expresar esto, utilizaremos las sucesiones exactas. \begin{definicion} Diremos que una expresión del siguiente estilo: @@ -708,6 +714,10 @@ urlcolor=black]{hyperref} \section{Producto Exterior} De cara a la demostración del Criterio de Saito, utilizaremos una operación que nos + \cite{SINGULAR} + \todo[inline]{Demostrar que Der R es reflexivo. Propiedades de los modulos reflexivos (libre implica proyectivo implica reflexivo y los conversos condicionados), reflexivo implica libre de torsión, etc como esquema.} + \nocite{*} + \printbibliography \end{document} \ No newline at end of file diff --git a/bibliografia.bib b/bibliografia.bib new file mode 100644 index 0000000..e00f279 --- /dev/null +++ b/bibliografia.bib @@ -0,0 +1,64 @@ +@Book{SINGULAR, + shorthand = "Singular", + author="Gert-Martin Greuel and Gerhard Pfister", + title="A Singular Introduction to Commutative Algebra", + publisher = "Springer", + isbn = "978-3-540-73541-0", + edition = "2", + year = "2007", + doi = "https://doi.org/10.1007/978-3-540-73542-7" +} +@Book{COCOA, + shorthand = "CoCoA1", + author= "Martin Kreuzer and Lorenzo Robbiano", + title= "Computational Commutative Algebra 1", + publisher= "Springer Berlin, Heidelberg", + year= "2000", + isbn= "978-3-540-67733-8", + doi= "https://doi.org/10.1007/978-3-540-70628-1" +} +@Book{IDEALS, + shorthand = {IdVaAl}, + author = {David A. Cox and John Little and Donal O'Shea}, + title = {Ideals, Varieties and Algorithms}, + edition = {4}, + publisher = {Springer Cham}, + year = {2015}, + isbn = {978-3-319-16720-6}, + doi = {https://doi.org/10.1007/978-3-319-16721-3}, + series = {Undergraduate Texts in Mathematics} + } +% El lugar donde se puede encontrar publicado el artículo de Saito es aquí: https://repository.dl.itc.u-tokyo.ac.jp/records/39646. +@article{SAITO, + shorthand = {Saito}, + author = {Saito, Kyoji}, + year = {1980}, + month = {01}, + pages = {265-291}, + title = {Theory of logarithmic differential forms and logarithmic vector fields}, + journal = {Journal of the Faculty of Science (sección 1A)}, + publisher = {Universidad de Tokio}, + volume = {27}, + number = {2}, + issn = {00408980}, + url = {https://repository.dl.itc.u-tokyo.ac.jp/records/39646}, + urldate = {2025-05-28} +} +@misc{VALLES, + shorthand = {Faenzi}, + title={Saito criterion and its avatars}, + author={Daniele Faenzi and Marcos Jardim and Jean Vallès}, + year={2024}, + eprint={2402.08305}, + archivePrefix={arXiv}, + primaryClass={math.AG}, + url={https://arxiv.org/abs/2402.08305}, +} +@online{STACKS, + shorthand = {Stacks}, + author = {The {Stacks Project Authors}}, + title = {\textit{Stacks Project}}, + url = {https://stacks.math.columbia.edu}, + urldate = {2025-05-28}, + year = {2025} +}