Previous Special Year Seminar

Let p be an odd prime number and let F be a totally real field. Let F_cyc be the cyclotomic extension of F generated by the roots of unity of order a power of p . From the maximal abelian extension of F_cyc which is unramified (resp. unramified...

Let $\overline K$ be an algebraic closure of a $p$-adic field $K$. We construct a separated noetherian regular scheme $X$ (nonalgebraic) equipped with an action of $G_K=\mathrm{Gal}(\overline{K}/K)$. We have $H^0(X, O_X) = Q_p$ and $H_1(X, O_X) = 0$...

The cohomology of arithmetic groups (with real coefficients) is usually understood in terms of automorphic forms. Such methods, however, fail (at least naively) to capture information about torsion classes in integral cohomology. We discuss a...

The cohomology of arithmetic groups (with real coefficients) is usually understood in terms of automorphic forms. Such methods, however, fail (at least naively) to capture information about torsion classes in integral cohomology. We discuss a...

This is an exposition of work on Artin's Conjecture on the zeros of p-adic forms.A variety of lines of attack are described ,going back to 1945.However there is particular emphasis on recent developments concerning quartic forms on the one hand ,and...

The Ramanujan conjecture states that for a holomorphic cusp form $f(z) =\sum_{n \in N} \lambda_f(n)e(nz)$ of weight $k$, the coefficients $\lambda_f(n)$ satisfy the bound $|\lambda_f(n)| \ll_\epsilon n^{(k−1)/2+\epsilon}$. In the case where $k$ is...