Gau{\ss}-Manin determinant connections and periods for irregular connections

Gau{\ss}-Manin determinant connections associated to irregular connections on a curve are studied. The determinant of the Fourier transform of an irregular connection is calculated. The determinant of cohomology of the standard rank 2 Kloosterman sheaf is computed modulo 2 torsion. Periods associated to irregular connections are studied in the very basic $\exp (f)$ case, and analogies with the Gau{\ss}-Manin determinant are discussed.