# Fdb version 3 ["pdflatex"] 1560365538 "main.tex" "main.pdf" "main" 1560365539 "/etc/texmf/web2c/texmf.cnf" 1535314180 475 c0e671620eb5563b2130f56340a5fde8 "" "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1511824771 3332 103109f5612ad95229751940c61aada0 "" "/usr/share/texlive/texmf-dist/fonts/tfm/adobe/palatino/pplb7t.tfm" 1480098688 1616 371d1ee60c04b008c8fd760060cd34f1 "" "/usr/share/texlive/texmf-dist/fonts/tfm/adobe/palatino/pplb8t.tfm" 1480098688 3456 16dd534f88eb2bd21ebc7203786b436e "" "/usr/share/texlive/texmf-dist/fonts/tfm/adobe/palatino/pplr7t.tfm" 1480098688 1804 7b5f73028f6509167f47ace9d69509ed "" "/usr/share/texlive/texmf-dist/fonts/tfm/adobe/palatino/pplr8t.tfm" 1480098688 3820 ee5b9d58608ae328e43c6e2bfd4ff851 "" "/usr/share/texlive/texmf-dist/fonts/tfm/jknappen/ec/ecrm1000.tfm" 1480098696 3584 adb004a0c8e7c46ee66cad73671f37b4 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msam10.tfm" 1480098698 916 f87d7c45f9c908e672703b83b72241a3 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/symbols/msbm10.tfm" 1480098698 908 2921f8a10601f252058503cc6570e581 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/mathpazo/zplmb7m.tfm" 1480098713 2100 38b16244127c37b323d93d4fdd707706 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/mathpazo/zplmb7t.tfm" 1480098713 1640 c14e51df62d6cb0dd79e4ca3b91ca7c3 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/mathpazo/zplmb7y.tfm" 1480098713 1308 6491569d9c934446101cd9b90e2a8e47 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/mathpazo/zplmr7m.tfm" 1480098713 2080 40a71f65088bdd047622ce295520749e "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/mathpazo/zplmr7t.tfm" 1480098713 1828 bb8add3bd19426549f9267c88b0cb8bd "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/mathpazo/zplmr7v.tfm" 1480098713 1012 955c4ca523d7827d33db91a33412b048 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/mathpazo/zplmr7y.tfm" 1480098713 1316 b4037e9c09961a72f8476628774e1ec1 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs10.tfm" 1480098717 688 37338d6ab346c2f1466b29e195316aa4 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/rsfs/rsfs5.tfm" 1480098717 684 3a51bd4fd9600428d5264cf25f04bb9a "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyatip10.tfm" 1480098719 608 50246cc71b0635b0ba0a5c10a0bf4257 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybsql10.tfm" 1480098719 608 4db60f15ea23b4ec2d796c6d568a63fa "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xybtip10.tfm" 1480098719 608 50246cc71b0635b0ba0a5c10a0bf4257 "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycirc10.tfm" 1480098719 844 3393210079fb4ed9347e214b3bfd7c1a "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmat10.tfm" 1480098719 608 f124f78ed50a1817738d2adb190cf2bd "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xycmbt10.tfm" 1480098719 608 f124f78ed50a1817738d2adb190cf2bd "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xydash10.tfm" 1480098719 984 5c01c46b93e3ba8369f3f8edc6e62aef "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xyluat10.tfm" 1480098719 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" "/usr/share/texlive/texmf-dist/fonts/tfm/public/xypic/xylubt10.tfm" 1480098719 608 a3a3bc08980c5126ff2a7a68fb5a64ff "" "/usr/share/texlive/texmf-dist/tex/context/base/mkii/supp-pdf.mkii" 1480098806 71627 94eb9990bed73c364d7f53f960cc8c5b "" "/usr/share/texlive/texmf-dist/tex/generic/ifxetex/ifxetex.sty" 1480098815 1458 43ab4710dc82f3edeabecd0d099626b2 "" "/usr/share/texlive/texmf-dist/tex/generic/oberdiek/gettitlestring.sty" 1480098815 8237 3b62ef1f7e2c23a328c814b3893bc11f "" "/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-generic.sty" 1517006633 185082 6c11d4e30ed78e2a12957b7e77030856 "" "/usr/share/texlive/texmf-dist/tex/generic/oberdiek/hobsub-hyperref.sty" 1480098815 70864 bcd5b216757bd619ae692a151d90085d "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xy.sty" 1480098819 4692 1e1bcf75c622af1eefd9169948208302 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xy.tex" 1480098819 115380 413d5f789929a45aab7d12ce0d0aee7d "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyall.tex" 1480098819 1449 24340b6befc66d28ee1ebb657efb5892 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyarrow.tex" 1480098819 22657 990ce136a3cc15728ba417a2e78b25c8 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycmtip.tex" 1480098819 1374 43fb8dc80dd748631d78096701166d76 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycolor.tex" 1480098819 4586 edd672434f45626662368282c0322160 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xycurve.tex" 1480098819 109670 d412ee1ff259daefee5e927172e2f9a8 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyframe.tex" 1480098819 24249 186931a828664624939ab0b347e3952c "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xygraph.tex" 1480098819 9619 b7e4d9a6936ba2ad6119a280abde9641 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyidioms.tex" 1480098819 2907 1ee562fde0b53c9cd16f7a604f33fdf0 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyline.tex" 1480098819 10928 c3a572983ccc9fc596b4e9ce454d5652 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xymatrix.tex" 1480098819 22583 25b1e7edeee41f181ee9733429da4a9c "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-co.tex" 1480098819 8442 90cb8a3b00c2081384c1ce988d2ba0a3 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-cu.tex" 1480098819 39762 25a964ebb390bcfcd35c040f477eef1d "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-fr.tex" 1480098819 16485 5686b19cc46d046c885428794ed9c114 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-li.tex" 1480098819 2619 1a12b316e2132654e44ba2cd21def637 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf-ro.tex" 1480098819 5290 e16fc85c85f64d0a5c04708bf3312d00 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xypdf.tex" 1480098819 18763 e61049d36bdfccb226f22e582d70d368 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyrecat.tex" 1480098819 1391 c8763fc8e281cb6ecf697988b6608e4a "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xyrotate.tex" 1480098819 7008 cb768d8d63a12d35607cbb3c4e7ba163 "" "/usr/share/texlive/texmf-dist/tex/generic/xypic/xytips.tex" 1480098819 3689 0d51788a4141bc66ab896f7ac63495fd "" "/usr/share/texlive/texmf-dist/tex/latex/amscls/amsthm.sty" 1513722769 12604 3dec726c041422879dc3268237f09026 "" "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amsfonts.sty" 1480098820 5949 3f3fd50a8cc94c3d4cbf4fc66cd3df1c "" "/usr/share/texlive/texmf-dist/tex/latex/amsfonts/amssymb.sty" 1480098820 13829 94730e64147574077f8ecfea9bb69af4 "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty" 1480098820 2210 5c54ab129b848a5071554186d0168766 "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty" 1480098820 4160 c115536cf8d4ff25aa8c1c9bc4ecb79a "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty" 1504905757 84352 897a476d96a0681047a5b0f91178a3d2 "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty" 1480098820 4115 318a66090112f3aa3f415aeb6fe8540f "" "/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty" 1480098820 2431 fe3078ec12fc30287f568596f8e0b948 "" "/usr/share/texlive/texmf-dist/tex/latex/base/article.cls" 1480098821 19821 310da678527a7dfe2a02c88af38079b7 "" "/usr/share/texlive/texmf-dist/tex/latex/base/fixltx2e.sty" 1492297155 15510 1c4e54b5314ada40f53d6cb0c6970568 "" "/usr/share/texlive/texmf-dist/tex/latex/base/fontenc.sty" 1492297155 4571 13977df0eda144b93597fc709035ad1f "" "/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty" 1480098821 4732 d63eda807ac82cca2ca8488efd31a966 "" "/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu" 1487721667 2004 ac51aeac484f08c01026120d62677eca "" "/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu" 1487721667 3181 1cb3e9ad01f4a01127b2ffd821bfeec7 "" "/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo" 1480098821 8292 e897c12e1e886ce77fe26afc5d470886 "" "/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.def" 1492297155 10006 a90ba4035cf778f32f424e297d92e235 "" "/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu" 1487721667 11255 9d97362866549d3d3c994b5f28d1b9b5 "" "/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def" 1487721667 7784 325a2a09984cb5c4ff230f9867145ad3 "" "/usr/share/texlive/texmf-dist/tex/latex/braket/braket.sty" 1480098823 3601 193635d942bc4777a5acaaeeffdce692 "" "/usr/share/texlive/texmf-dist/tex/latex/cleveref/cleveref.sty" 1518215819 326269 43f5464dd8dfbb221892d3649dfc6f72 "" "/usr/share/texlive/texmf-dist/tex/latex/etex-pkg/etex.sty" 1480098827 19013 c49da619eb7bd8093706fabc7ba9ceae "" "/usr/share/texlive/texmf-dist/tex/latex/fancyhdr/fancyhdr.sty" 1498861448 10663 d7fcc0dc4f35e8998b8cfeef8407d37d "" "/usr/share/texlive/texmf-dist/tex/latex/float/float.sty" 1480098828 6749 16d2656a1984957e674b149555f1ea1d "" "/usr/share/texlive/texmf-dist/tex/latex/framed/framed.sty" 1480098829 22449 7ec15c16d0d66790f28e90343c5434a3 "" "/usr/share/texlive/texmf-dist/tex/latex/geometry/geometry.sty" 1480098829 40502 e003406220954b0716679d7928aedd8a "" "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/color.cfg" 1480098830 1213 620bba36b25224fa9b7e1ccb4ecb76fd "" "/usr/share/texlive/texmf-dist/tex/latex/graphics-cfg/graphics.cfg" 1480098830 1224 978390e9c2234eab29404bc21b268d1e "" "/usr/share/texlive/texmf-dist/tex/latex/graphics-def/pdftex.def" 1515537368 17334 520b9b85ad8a2a48eda3f643e27a5179 "" "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphics.sty" 1498427532 15275 7d676729b1bedd3e7f3c6717affb366c "" "/usr/share/texlive/texmf-dist/tex/latex/graphics/graphicx.sty" 1498427532 9066 649f2ccf62888e3d8c3e57256b70b8e1 "" "/usr/share/texlive/texmf-dist/tex/latex/graphics/keyval.sty" 1480098830 2594 d18d5e19aa8239cf867fa670c556d2e9 "" "/usr/share/texlive/texmf-dist/tex/latex/graphics/trig.sty" 1480098830 3980 0a268fbfda01e381fa95821ab13b6aee "" "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hpdftex.def" 1518041854 51699 9069fc983fff0db91d59a15af144ad62 "" "/usr/share/texlive/texmf-dist/tex/latex/hyperref/hyperref.sty" 1518041854 234088 2c849389d62d41c593d9f5176c4116ab "" "/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty" 1480098831 12949 81e4e808884a8f0e276b69410e234656 "" "/usr/share/texlive/texmf-dist/tex/latex/hyperref/pd1enc.def" 1518041854 14098 4e70bf396c7c265bd8b0e5cab3fd3d4d "" "/usr/share/texlive/texmf-dist/tex/latex/jknapltx/mathrsfs.sty" 1480098831 300 12fa6f636b617656f2810ee82cb05015 "" "/usr/share/texlive/texmf-dist/tex/latex/jknapltx/ursfs.fd" 1480098831 548 cc4e3557704bfed27c7002773fad6c90 "" "/usr/share/texlive/texmf-dist/tex/latex/latexconfig/epstopdf-sys.cfg" 1480098833 678 4792914a8f45be57bb98413425e4c7af "" "/usr/share/texlive/texmf-dist/tex/latex/latexconfig/hyperref.cfg" 1480098833 235 6031e5765137be07eed51a510b2b8fb7 "" "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.cfg" 1480098833 1827 d72ad54409ca5c1068a1939c63441bd2 "" "/usr/share/texlive/texmf-dist/tex/latex/listings/listings.sty" 1480098833 80336 ff90c926c3d7bfdaa3d80ca57123b0bb "" "/usr/share/texlive/texmf-dist/tex/latex/listings/lstmisc.sty" 1480098833 77028 c3eb00afb55a32bc13ca8da7f5234377 "" "/usr/share/texlive/texmf-dist/tex/latex/marvosym/marvosym.sty" 1480098833 9393 ceaf2ea8eb2c81fdb168323fc5fffc89 "" "/usr/share/texlive/texmf-dist/tex/latex/mathtools/mathtools.sty" 1515449928 53430 0411f0481da6078e76fd7de46531d2e0 "" "/usr/share/texlive/texmf-dist/tex/latex/mathtools/mhsetup.sty" 1496786006 5317 cf75154a8a7e6436f05a5be497f0b05e "" "/usr/share/texlive/texmf-dist/tex/latex/multirow/multirow.sty" 1480201744 5015 cd8d25106b58dfc16af57528a07d0bc9 "" "/usr/share/texlive/texmf-dist/tex/latex/oberdiek/auxhook.sty" 1480098836 3834 4363110eb0ef1eb2b71c8fcbcdb6c357 "" "/usr/share/texlive/texmf-dist/tex/latex/oberdiek/epstopdf-base.sty" 1480098836 12095 5337833c991d80788a43d3ce26bd1c46 "" "/usr/share/texlive/texmf-dist/tex/latex/oberdiek/grfext.sty" 1480098836 7075 2fe3d848bba95f139de11ded085e74aa "" "/usr/share/texlive/texmf-dist/tex/latex/oberdiek/kvoptions.sty" 1480098836 22417 1d9df1eb66848aa31b18a593099cf45c "" "/usr/share/texlive/texmf-dist/tex/latex/oberdiek/rerunfilecheck.sty" 1480098836 9581 023642318cef9f4677efe364de1e2a27 "" "/usr/share/texlive/texmf-dist/tex/latex/placeins/placeins.sty" 1480098837 4087 636308456f60d2b31cbf97867db5708d "" "/usr/share/texlive/texmf-dist/tex/latex/psnfss/mathpazo.sty" 1480098837 8977 7001b1ab94674ce4a6004aef2826ec90 "" "/usr/share/texlive/texmf-dist/tex/latex/psnfss/omlzplm.fd" 1480098837 638 2349dd185efcefd0c3380a2601df0cee "" "/usr/share/texlive/texmf-dist/tex/latex/psnfss/omszplm.fd" 1480098837 455 c09241d92b40b1b84eb2bb5776606aea "" "/usr/share/texlive/texmf-dist/tex/latex/psnfss/omxzplm.fd" 1480098837 322 fb88cb3e5f25cf1596ba8826c4210e0e "" "/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1ppl.fd" 1480098837 961 06b773644d960aac68add40fcb596208 "" "/usr/share/texlive/texmf-dist/tex/latex/psnfss/ot1zplm.fd" 1480098837 436 5e7baa1a259bab50a2bdffad6426f38c "" "/usr/share/texlive/texmf-dist/tex/latex/psnfss/t1ppl.fd" 1480098837 774 5747d3f33ec2f7c4881c94e931a130b1 "" "/usr/share/texlive/texmf-dist/tex/latex/titlesec/titlesec.sty" 1480098841 37387 afa86533e532701faf233f3f592c61e0 "" "/usr/share/texlive/texmf-dist/tex/latex/titling/titling.sty" 1480098841 7358 95ac619994bd30d405a74f3eca431c84 "" "/usr/share/texlive/texmf-dist/tex/latex/tools/bm.sty" 1485129666 12628 f9caa46b01869ce6fad7de6138318b70 "" "/usr/share/texlive/texmf-dist/tex/latex/tools/calc.sty" 1480098841 10214 d03d065f799d54f6b7e9b175f8d84279 "" "/usr/share/texlive/texmf-dist/tex/latex/tools/enumerate.sty" 1480098841 3467 d39e40f25d5fd2b3b49a58d155063dd6 "" "/usr/share/texlive/texmf-dist/tex/latex/url/url.sty" 1480098842 12796 8edb7d69a20b857904dd0ea757c14ec9 "" "/usr/share/texlive/texmf-dist/tex/latex/wrapfig/wrapfig.sty" 1480098843 26220 3701aebf80ccdef248c0c20dd062fea9 "" "/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty" 1480098843 55589 34128738f682d033422ca125f82e5d62 "" "/usr/share/texlive/texmf-dist/web2c/texmf.cnf" 1520210507 32485 c64754543d8ac501bea6e75e209ea521 "" "/usr/share/texmf/web2c/texmf.cnf" 1520210507 32485 c64754543d8ac501bea6e75e209ea521 "" "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1539447059 4126370 04448162a4da151233589cc4b45c1165 "" "contents/classical_graded_rings.tex" 0 -1 0 "" "main.aux" 1560365539 662 b2b94621371df8d9296b8bf5bec1b851 "" "main.out" 1560365539 0 d41d8cd98f00b204e9800998ecf8427e "" "main.tex" 1516782458 4463 cc7fef970f854158c6735258d208200c "" "main.toc" 1560365539 0 d41d8cd98f00b204e9800998ecf8427e "" (generated) "main.log" "main.aux" "main.toc" "main.out" "main.pdf"