Sage Days 21: Function Fields Reading List

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Reading List

Drinfeld Modules and Modular Varieties:

• Boeckle Arithmetic over function fields (a cohomological approach). Number fields and function fields---two parallel worlds, 1--38, Progr. Math., 239.

• Buthenuth, Some writeups on computing quaternion quotient graphs. unpublished notes.

• Gekeler and Nonnengardt, Fundamental domains of some arithmetic groups over function fields. Internat. J. Math. 6 (1995), no. 5, 689--708.

• Gekeler and Reversat, Jacobians of Drinfeld modular curves. J. Reine Angew. Math. 476 (1996), 27--93.

• Hall, Fundamental domains of some Drinfeld modular curves. unpublished manuscript.

• Papikian, Computation of Heegner Points for Function Fields. Notes from the 2000 Arizona Winter School (A note from the author: "Please keep in mind that I wrote those notes when I was just learning the subject, so they might contain some mistakes.")

• Vleduts and Manin, Linear codes and modular curves. (English translation of) Current problems in mathematics, Vol. 25, 209--257

Elliptic Surfaces:

• Roberts, Explicit Descent On Elliptic Curves Over Function Fields. PhD Thesis, University of Nottingham, 2007.

• Ulmer, Elliptic curves with large rank over function fields. Ann. of Math. (2) 155 (2002), no. 1, 295--315.

• Ulmer, Elliptic curves and analogies between number fields and function fields. Heegner points and Rankin L-series, 285--315, Math. Sci. Res. Inst. Publ., 49, Cambridge Univ. Press, Cambridge, 2004.

• Ulmer, $L$-functions with large analytic rank and abelian varieties with large algebraic rank over function fields. Invent. Math. 167 (2007), no. 2, 379--408.

Modular Symbols:

• Armana, Torsion rationnelle des modules de Drinfeld. (French) PhD. thesis.

• Darmon, Pollack, The efficient calculation of Stark-Heegner points via overconvergent modular symbols. Israel J. Math. 153 (2006), 319--354.

• Gekeler, On the cuspidal divisor class group of a Drinfeld modular curve. Doc. Math. 2 (1997), 351--374 (electronic).

• Merel, Universal fourier expansions of modular forms. On Artin's conjecture for odd 2-dimensional representations, 59--94, Lecture Notes in Math., 1585, Springer.

• Reversat, Sur les revetements de Schottky des courbes modulaires de Drinfeld. Arch. Math. (Basel) 66 (1996), no. 5, 378--387.

• Teitelbaum, Modular symbols for $\mathbb{F}_q[t]$. Duke Math. J. 68 (1992), no. 2, 271--295.