Papers to Read

Algebraic Topology

Read classical papers by Adams, Pontryagin, Quillen, Serre, Sullivan, Thom. John Francis has a list of classical papers for the Kan seminar on his homepage.

A big list: https://cpb-us-e1.wpmucdn.com/s.wayne.edu/dist/0/60/files/2019/08/List-of-papers.pdf
Another big list: https://cpb-us-e1.wpmucdn.com/s.wayne.edu/dist/0/60/files/2019/08/List-of-papers-2.pdf
Algebraic Topology, The Kan Seminar https://ocw.mit.edu/courses/mathematics/18-915-graduate-topology-seminar-kan-seminar-fall-2014/reading-list/list-of-possible-papers/ #resources/papers
- https://math.vanderbilt.edu/bohmanar/literature.pdf

Serre, J. -P. “http://dx.doi.org/10.1007/BF02564562)." Commentarii Mathematici Helvetici 27, no. 1 (1953." Commentarii Mathematici Helvetici 27, no. 1 (1953): 198-232.

Thom, R. “http://dx.doi.org/10.1007/BF02566923)." Commentarii Mathematici Helvetici 28 (1954." Commentarii Mathematici Helvetici 28 (1954): 17-86.

Milnor, J. W. “On the Construction FK.” In Algebraic Topology: A Student’s Guide (London Mathematical Society Lecture Note). Vol. 4. Cambridge University Press, 1972, pp. 119-36. ISBN: 9780521080767.

———. “http://www.jstor.org/stable/1969983)." Annals of Mathematics 64, no. 2 (1956." Annals of Mathematics 64, no. 2 (1956): 399-405.

Milnor, J. W., and J. D. Stasheff. Characteristic Classes (Annals of Mathematics Studies). Vol. 76_._ Princeton University Press, 1974. ISBN: 9780691081229. \begin{align*}[http://books.google.com/books?id=5zQ9AFk1i4EC&pg=PAfrontcover]]\end{align*}

Milnor, J. W. “http://www.jstor.org/stable/1969967)." Annals of Mathematics 65, no. 2 (1957." Annals of Mathematics 65, no. 2 (1957): 357-62.

Moore, J. C. “Semi-simplicial complexes and Postnikov systems.” In Symposium Internacional de Topologia Algebraica. La Universidad Nacional Autonoma de Mexico y la UNESCO, 1958, pp. 232-47.

Bott, R. “http://www.jstor.org/stable/1970106)." Annals of Mathematics 70, no. 2 (1959." Annals of Mathematics 70, no. 2 (1959): 313-37.

Adams, J. F. “http://www.jstor.org/stable/1970147)." Annals of Mathematics 72, no. 1 (1960." Annals of Mathematics 72, no. 1 (1960): 20-104.

———. “http://www.jstor.org/stable/1970213)." Annals of Mathematics 75, no. 3 (1962." Annals of Mathematics 75, no. 3 (1962): 603-32.

Brown, E. H., Jr. “http://www.jstor.org/stable/1970209)." Annals of Mathematics 75, no. 3 (1962." Annals of Mathematics 75, no. 3 (1962): 467-84.

Kervaire, M. A., and J. W. Milnor. “http://www.jstor.org/stable/1970128)." Annals of Mathematics 77, no. 3 (1963." Annals of Mathematics 77, no. 3 (1963): 504-37.

Atiyah, M. F. K-theory (Advanced Book Classics). 2nd ed. Notes by D. W. Anderson. Addison Wesley Longman Publishing Company, 1989. ISBN: 9780201093940.

Wall, C. T. C. “http://www.jstor.org/stable/1970382)." Annals of Mathematics 81, no. 1 (1965." Annals of Mathematics 81, no. 1 (1965): 56-69.

Adams, J. F. “http://dx.doi.org/10.1016/0040-9383(66)90004-8)." Topology 5, no. 1 (1966." Topology 5, no. 1 (1966): 21-71.

Adams, J. F., and M. F. Atiyah. http://dx.doi.org/10.1093/qmath/17.1.31)." The Quarterly Journal of Mathematics 17, no. 1 (1966." The Quarterly Journal of Mathematics 17, no. 1 (1966): 31-38.

Quillen, D. G. Homotopical Algebra (Lecture Notes in Mathematics). Vol. 43. Springer, 1967. ISBN: 9783540039143.

Segal, G. “http://dx.doi.org/10.1007/BF02684591)." Publications Math´ematiques de I’lnstitut Hautes des E’tudes Scientifique 34, no. 1 (1968." Publications Math´ematiques de I’lnstitut Hautes des E’tudes Scientifique 34, no. 1 (1968): 105-12.

Atiyah, M. F., and G. Segal. “Equivariant K-theory and Completion.” Journal of Differential Geometry 3, no. 1-2 (1969): 1-18.

Adams, J. F. “Quillen’s Work on Formal Groups and Complex Cobordism.” In Stable Homotopy and Generalised Homology (Chicago Lectures in Mathematics). University of Chicago Press, 1995. ISBN: 9780226005249. \begin{align*}reprint of the 1974 original\end{align*}

Quillen, D. G. “http://www.jstor.org/stable/1970770)." Annals of Mathematics 94, no. 3 (1971." Annals of Mathematics 94, no. 3 (1971): 549-72.

May, J. P. The Geometry of Iterated Loop Spaces (Lectures Notes in Mathematics). Vol. 271. Springer-Verlag, 1972.

Quillen, D. G. “http://www.jstor.org/stable/1970825)." Annals of Mathematics 96, no. 3 (1972." Annals of Mathematics 96, no. 3 (1972): 552-86.

———. “Algebraic K-theory I.” In Higher K-Theories (Lecture Notes in Mathematics). Vol. 341. Springer, 1973, pp. 85-147. ISBN: 9783540064343.

Nishida, G. “http://dx.doi.org/10.2969/jmsj/02540707)." Journal of the Mathematical Society of Japan 25, no. 4 (1973." Journal of the Mathematical Society of Japan 25, no. 4 (1973): 707-32.

Adams, J. F. Stable Homotopy and Generalised Homology (Chicago Lectures in Mathematics). University of Chicago Press, 1995. ISBN: 9780226005249. \begin{align*}reprint of the 1974 original\end{align*}

Segal, G. “http://dx.doi.org/10.1016/0040-9383(74)90022-6)." Topology 13, no. 3 (1974." Topology 13, no. 3 (1974): 293-312.

Bousfield, A. K. “http://dx.doi.org/10.1016/0040-9383(75)90023-3)." Topology 14, no. 2 (1975." Topology 14, no. 2 (1975): 133-50.

Griffiths, P. A., and J. W. Morgan. Rational Homotopy Theory and Differential Forms. Birkh ̈auser, 1981. ISBN: 9783764330415.

Adams, J. F. “Prerequisites (on equivariant stable homotopy theory) for Carlsson’s lecture.” In Algebraic Topology (Lecture Notes in Mathematics). Vol. 1051. Springer-Verlag, 1984, pp. 483-532. ISBN: 9780387129020.

Waldhausen, F. “Algebraic K-theory of Spaces.” In Algebraic and Geometric Topology (Lecture Notes in Mathematics). Vol. 1126. Springer, 1985, pp. 318-419. ISBN: 9783540152354.

Atiyah, M. F. Thom complexes. Proc. London Math. Soc. (3) 11 1961 291–310.
Adams, J. F. Vector fields on spheres. Ann. of Math. (2) 75 1962 603–632.
Atiyah, M. F.; Segal, G. B. Equivariant \(K\)-theory and completion. J. Differential Geometry 3 1969 1–18.
Atiyah, M. F.; Singer, I. M. Index theory for skew-adjoint Fredholm operators. Inst. Hautes Études Sci. Publ. Math. No. 37 1969 5–26.
Quillen, Daniel Elementary proofs of some results of cobordism theory using Steenrod operations. Advances in Math. 7 1971 29–56 (1971).
Segal, Graeme Categories and cohomology theories. Topology 13 (1974), 293–312.
Snaith, V. P. A stable decomposition of \(\\Omega \\sp{n}S\\sp{n}X\). J. London Math. Soc. (2) 7 (1974), 577–583.
Sullivan, Dennis Genetics of homotopy theory and the Adams conjecture. Ann. of Math. (2) 100 (1974), 1–79.
Bousfield, A. K. The localization of spaces with respect to homology. Topology 14 (1975), 133–150.
McDuff, D.; Segal, G. Homology fibrations and the ``group-completion’’ theorem. Invent. Math. 31 (1975/76), no. 3, 279–284.
Mahowald, Mark A new infinite family in \({}\\sb{2}\\pi\\sb {\*}{}\\sp s\). Topology 16 (1977), no. 3, 249–256.
Miller, Haynes R.; Ravenel, Douglas C.; Wilson, W. Stephen Periodic phenomena in the Adams-Novikov spectral sequence. Ann. Math. (2) 106 (1977), no. 3, 469–516.
Kahn, Daniel S.; Priddy, Stewart B. The transfer and stable homotopy theory. Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 103–111.
Bousfield, A. K. The localization of spectra with respect to homology. Topology 18 (1979), no. 4, 257–281.
Dwyer, W. G.; Kan, D. M. Simplicial localizations of categories. J. Pure Appl. Algebra 17 (1980), no. 3, 267–284.
Miller, Haynes R. On relations between Adams spectral sequences, with an application to the stable homotopy of a Moore space. J. Pure Appl. Algebra 20 (1981), no. 3, 287–312.
Cohen, F. R.; May, J. P.; Taylor, L. R. \(K(Z,\\,0)\) and \(K(Z\\sb{2},\\,0)\) as Thom spectra. Illinois J. Math. 25 (1981), no. 1, 99–106.
Adams, J. F. Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture. Algebraic topology, Aarhus 1982 (Aarhus, 1982), 483–532, Lecture Notes in Math., 1051, Springer, Berlin, 1984.
Jardine, J. F. Simplicial presheaves. J. Pure Appl. Algebra 47 (1987), no. 1, 35–87.
Morava, Jack Forms of \(K\)-theory. Math. Z. 201 (1989), no. 3, 401–428.
Martino, John; Priddy, Stewart The complete stable splitting for the classifying space of a finite group. Topology 31 (1992), no. 1, 143–156.
Aguilar, M. A.; Prieto, Carlos Quasifibrations and Bott periodicity. II Iberoamerican Conference on Topology and its Applications (Morelia, 1997). Topology Appl. 98 (1999), no. 1-3, 3–17.

Algebraic Geometry

Abramovich, Temkin, and Włodarczyk: Functorial embedded resolution via weighted blowings up
Araujo, Druel, Kovács: Cohomological characterizations of projective spaces and hyperquadrics.
Bayer, Lahoz, Macrì, Nuer, Perry, and Stellari: Stability conditions in families
Bhatt: On the direct summand conjecture and its derived variant
Birkar, Cascini, Hacon, McKernan: Existence of minimal models for varieties of log general type
Blanc and Cantat: Dynamical degrees of birational transformations of projective surfaces.
Blekherman, Smith, Velasco: Sums of squares and varieties of minimal degree.
Bondal and Orlov, Reconstruction of a variety from the derived category and groups of autoequivalences
Bridgeland: Stability conditions on triangulated categories
Cesnavicius and Scholze: Purity for flat cohomology
Eisenbud and Schreyer: Betti numbers of graded modules and cohomology of vector bundles.
Esnault and Mehta: Simply connected projective manifolds in characteristic p>0 have no nontrivial stratified bundles
Hassett, Pirutka, and Tschinkel: Stable rationality of quadric surface bundles over surfaces
Huh: Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs.
Kuznetsov, Homological projective duality
Laza, Saccà, Voisin: A hyper-Kähler compactification of the intermediate Jacobian fibration associated with a cubic 4-fold.
Maulik, Nekrasov, Okounkov, and Pandharipande: Gromov-Witten theory and Donaldson-Thomas theory. I & II
Nicaise and Shinder: The motivic nearby fiber and degeneration of stable rationality
Popa and Schnell: Kodaira dimension and zeros of holomorphic one-forms
Totaro: Hodge theory of classifying stacks.
Voisin: Unirational threefolds with no universal codimension 2 cycle

Adams Atiyah, K Theory and the Hopf Invariant