Seminar Darstellungstheorie

Das Seminar Darstellungstheorie findet normalerweise dienstags, 14.15 - 15.15 Uhr in G.13.18 statt.

Beteiligte Dozenten: Sascha Orlik, Kay Rülling, Tobias Schmidt, Britta Späth.

Wang: Representations of SL_2(F_q) via crystalline cohomology

Let C be the projective plane curve given by xy^q-x^qy-z^{q+1}. Drinfeld proved that the discrete series representations of SL_2(F_q) arise in the l-adic cohomology of C. Analogously, the crystalline cohomology group H^1(C) is a Z_p-module, which carries actions of SL_2(F_q), a non-split torus, and the Frobenius endomorphism. Haastert and Jantzen constructed a filtration of H^1(C) by taking the preimage under the Frobenius endomorphism of the natural filtration of H^1(C) by pH^1(C), p^2H^1(C),.... In this talk, we explain the explicit computations of this filtration and the actions on H^1(C) following the papers of Haastert and Jantzen.

• Seminar Darstellungstheorie vergangener Semester