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Publications

# Title Coauthors arXiv link Journal
The foundation of generalized parallel connections, 2-sums, and segment-cosegment exchanges of matroids Matthew Baker, Zach Walsh, Tianyi Zhang arXiv:2404.10656 Preprint
Quiver matroids -- Matroid morphisms, quiver Grassmannians, their Euler characteristics and F1-points Manoel Jarra, Eduardo Vital arXiv:2404.09255 Preprint
New building blocks for F1-geometry: bands and band schemes Matthew Baker, Tong Jin arXiv:2402.09612 Preprint
Automorphic Forms for PGL(3) over elliptic function fields. Part 1: Graphs of Hecke operators Roberto Alvarenga, Valdir Pereira Junior arXiv:2107.08375 Preprint
Foundations of matroids II: Further theory, examples, and computational methods Matthew Baker, Tianyi Zhang arXiv:2310.19952 To appear in Combinatorial Theory
Foundations of matroids I: Matroids without large uniform minors Matthew Baker arXiv:2008.00014 To appear in Memoirs Amer. Math. Soc.
Mean payoff games with the signature of a potential Marianne Akian, Stéphane Gaubert, Matthias Mnich download Unpublished version
Lift theorems for representations of matroids over pastures Matthew Baker arXiv:2107.00981 J. Combin. Theory Ser. B, 170:1-55, 2025
Flag matroids with coefficients Manoel Jarra arXiv:2204.04658 Adv. Math. 436:109396, 2024
The topological shadow of F1-geometry: congruences spaces Samarpita Ray arXiv:2305.12801 Math. Z., 306(2):30, 2024
Towards the horizons of Tits’s vision: on band schemes, crowds and F1-structures Koen Thas arXiv:2305.13809 Innov. Incidence Geom., 20(2-3):353–394, 2023
Higher balancing for locally tropically convex tropical varieties Emilio Peixoto arXiv:1903.07640 Manuscripta Math., 171(3-4):583-593, 2023
A unifying approach to tropicalization --- arXiv:1508.07949 Trans. Amer. Math. Soc., 376(5):3111-3189, 2023
Quiver Grassmannians of extended Dynkin type D - Part 2: Schubert decompositions and F-polynomials Thorsten Weist arXiv:1507.00395 Algebr. Represent. Theory, 26(2):359-409, 2023
Algebraic K-theory and Grothendieck-Witt theory of monoid schemes Jens Niklas Eberhardt, Matthew B. Young arXiv:2009.12636 Math. Z., 301(2):1407-1445,2022.
Tropical geometry over the tropical hyperfield --- arXiv:1907.01037 Rocky Mountain J. Math. 52(1):189-222, 2022.
Group completion in the K-theory and Grothendieck-Witt theory of proto-exact categories Jens Niklas Eberhardt, Matthew B. Young arXiv:2009.12635 J. Pure Appl. Algebra 226(8):Paper No. 107018, 32 pp, 2022
Factorizations of tropical and sign polynomials Alexander Agudelo arXiv:2005.12882 Indag. Math. (N.S.), 32(4):797-812, 2021
The moduli space of matroids Matthew Baker arXiv:1809.03542 Adv. Math., 390:Paper No. 107883, 118, 2021
Descartes' rule of signs, Newton polygons, and polynomials over hyperfields Matthew Baker arXiv:1811.04966 J. Algebra, 569:416-441, 2021
Representation type via Euler characteritics and singularieties of quiver Grassmannians Thorsten Weist arXiv:1706.00860 Bull. Lond. Math. Soc. 51(5):815-835. 2019
Quiver Grassmannians of extended Dynkin type D - Part 1: Schubert systems and decompositions into affine spaces Thorsten Weist arXiv:1507.00392 Mem. Amer. Math. Soc. 261(1258):v+78 pp, 2019
Plücker relations for quiver Grassmannians Thorsten Weist arXiv:1607.01058 Algebr. Represent. Theory, 22(1):211--218, 2019
The geometry of blueprints. Part II --- arXiv:1201.1324 Forum Math. Sigma 6, e20, 90pp., 2018
F1 for everyone --- arXiv:1801.05337 Jahresber. Dtsch. Math.-Ver. 120(2), 83-116, 2018
Quasicoherent sheaves on projective schemes over F1 Matt Szczesny arXiv:1602.05233 J. Pure Appl. Algebra 222(6):1337-1354, 2018
Cech cohomology over F1^2 Jaret Flores, Matt Szczesny arXiv:1511.06875 J. Algebra 485, 269-287, 2017
On the relation between hyperrings and fuzzy rings Jeffrey Giansiracusa, Jaiung Jun arXiv:1607.01973 Beitr. Algebr. Geom. 58(4), 735-764, 2017
Blue schemes as relative schemes after Toen and Vaquie --- arXiv:1212.3261 J. Algebra 482, 264-302, 2017
A blueprinted view on F1-geometry --- arXiv:1301.0083 In Absolute Arithmetic and F1-geometry. European Mathematical Society Publishing House, 2016
Schemes as functors on topological rings Cecília Salgado arXiv:1410.1948 J. Number Theory 159, 193-201, 2016
Schubert decompositions for quiver Grassmannians of tree modules --- arXiv:1309.3762 Algebra Number Theory 9(6), 1337-1362, 2015
Blueprints - towards absolute arithmetic? --- arXiv:1204.3129 J. Number Theory 144, 408-421, 2014
On Schubert decompositions of quiver Grassmannians --- arXiv:1210.5993 J. Geom. Phys. 76, 169-191, 2014
Toroidal automorphic forms for function fields --- arXiv:1012.3223 Israel J. Math. 194, no. 2, 555-596, 2013
Graphs of Hecke operators --- arXiv:1012.3513 Algebra Number Theory 7, no. 1, 19-61, 2013
Automorphic forms for elliptic function fields --- arXiv:1012.4825 Math. Z. 272, no. 3-4, 885-911, 2012
Projective geometry for blueprints Javier López Peña arXiv:1203.1665 C. R. Math. Acad. Sci. Paris 350, no. 9-10, 455-458, 2012
Toroidal automorphic forms, Waldspurger periods and double Dirichlet series Gunther Cornelissen arXiv:0906.5284 In Multiple Dirichlet series, L-functions and automorphic forms, 131-146, Progr. Math., 300, Birkhäuser/Springer, New York, 2012
Algebraic groups over the field with one element --- arXiv:0907.3824 Math. Z. 271, no. 1-2, 117-138, 2012
Sheaves and K-theory for F1-schemes Chenghao Chu, Rekha Santhanam arXiv:1010.2896 Adv. Math. 229, no. 4,2239-2286, 2012
The geometry of blueprints. Part I --- arXiv:1103.1745 Adv. Math. 229, no. 3, 1804-1846, 2012
Mapping F1-land: an overview of geometries over the field with one element Javier López Peña arXiv:0909.0069 In Noncommutative geometry, arithmetic, and related topics, 241-265, Johns Hopkins Univ. Press, Baltimore, MD, 2011
Torified varieties and their geometries over F1 Javier López Peña arXiv:0903.2173 Math. Z. 267, no. 3-4, 605-643, 2011
Functional equations for zeta functions of F1-schemes --- arXiv:1010.1754 C. R. Acad. Sci. Paris, Ser. I 348, 1143-1146, 2010
Toroidal automorphic forms for some function fields Gunther Cornelissen arXiv:0710.2994 Journal of Number Theory 129 (6), 1456-1463, 2009
Toroidal automorphic forms for function fields --- download Thesis, Utrecht, 2008
On the K-theory of graph C*-algebras Gunther Cornelissen, Matilde Marcolli arXiv:math/0606582 Acta Appl. Math. 102 (1), 57-69, 2008
Completeness and compactness for varieties over a local field --- arXiv:math/0410346 Arch. Math. 88 (4), 344-348, 2007