# Sage Days 21: Function Fields Reading List

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## Reading List

Drinfeld Modules and Modular Varieties:

Armana http://people.math.jussieu.fr/~armana/armana-coefficientsdmfhecke.pdf

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 unpublished notes.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 unpublished manuscript.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.

Descent:

Broumas, Effective $p$-descent. Compositio Math 107 (1997), 125--141.

Problems / Open Questions:

Gekeler, Problems for Sage Days. Private correspondence