L-functions and other arithmetic invariants of curves of genus greater than or equal to 3

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The main theme of the proposed project is to use techniques related to semistable reduction of curves to study resolution of singularities, in particular wild quotient singularities in dimension two. A central case arises from the study of smooth projective curves over a p-adic field. Here we search to relate a suitable semistable model of the curve to a regular model via a quotient construction. This construction gives rise to quotient singularities, and we propose new methods for resolving them. More generally, the goal is to extend this construction also to surfaces in equal characteristic p, and to higher dimension. We plan to use the results of this study to develop practical algorithms to compute semistable models of curves. We also expect to obtain a better insight into the structure of the quotient singularities arising in our work, and thus be able to algorithmically compute their resolution, in cases that were so far inaccessible to brute force calculation.