Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We study the structure of the stacks of twisted stable maps to the classifying stack of a finite group G—which we call the stack of twisted G-covers, or twisted G-bundles. For a suitable group Gwe show that the substack corresponding to admissible G-covers is a smooth projective fine moduli space. Dedicated to Steven L. Kleiman on the occasion of his 60th birthday.

Twisted Bundles and Admissible Covers

We construct a Teichmuller curve uniformized by a Fuchsian triangle group commensurable to �(m, n, ∞) for every m, n ≤ ∞. In most cases, for example when m 6 n and m or n is odd, the uniformizing group is equal to the triangle group �(m, n, ∞). Our construction includes the Teichmuller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find billiard tables that generate these Teich- muller curves. We interpret some of the so-called Lyapunov exponents of the Kontsevich-Zorich cocycle as normalized degrees of a natural line bundle on a Teichmuller curve. We determine the Lyapunov exponents for the Teichmuller curves we construct.

https://annals.math.princeton.edu/wp-content/uploads/annals-v172-n1-p03-p.pdf

Teichmuller curves, triangle groups, and Lyapunov exponents

We construct a Teichmueller curve uniformized by the Fuchsian triangle group (m,n,\infty) for every m<n. Our construction includes the Teichmueller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find Billiard tables that generate these Teichmueller curves. 
We interprete some of the so-called Lyapunov exponents of the Kontsevich--Zorich cocycle as normalized degrees of some natural line bundles on a Teichmueller curves. We determine the Lyapunov exponents for the Teichmueller curves we construct.

Teichmueller curves, triangle groups, and Lyapunov exponents

We discuss the enumeration of function fields and number fields by discriminant. We show that Malle’s conjectures agree with heuristics arising naturally from geometric computations on Hurwitz schemes. These heuristics also suggest further questions in the number field setting.

Counting extensions of function fields with bounded discriminant and specified Galois group

Let G=Dp be the dihedral group of order 2p, where p is an odd prime. Let k be an algebraically closed field of characteristic p. We show that any action of G on the ring k[[y]] can be lifted to an action on R[[y]], where R is some complete discrete valuation ring with residue field k and fraction field of characteristic 0

The local lifting problem for dihedral groups

We study Galois covers of the projective line branched at three points with bad reduction to characteristic p, under the condition that p exactly divides the order of the Galois group. As an application of our results, we prove that the field of moduli of such a cover is at most tamely ramified at p.

/pdf/three-point-covers-with-bad-reduction-233fqqctkg.pdf

Three point covers with bad reduction

Modular curves are quotients of the upper half-plane by congruence subgroups of SL2(ℤ). The most prominent examples are X 0 (N),X1 (N) and X(N), for N ≥ 1. Modular curves are also moduli spaces for elliptic curves endowed with a level structure. Therefore, they are defined over small number fields and have a rich arithmetic structure. Deligne and Rapoport [4] determine the reduction behavior of X 0 (p) and X 1 (p) at the prime p. Using this result, they prove a conjecture of Shimura saying that the quotient of the Jacobian of X 1 (p) by the Jacobian of X 0 (p) acquires good reduction over ℚ(ςp). Both the reduction result and its corollary have been generalized by Katz and Mazur [10] to arbitrary level N and various level structures.

Stable reduction of modular curves

Special covers are metacyclic covers of the projective line, with Galois group Z /p⋊ Z /m , which have a specific type of bad reduction to characteristic p. Such covers arise in the study of the arithmetic of Galois covers of  P 1 with three branch points. Our results provide a simple description of special covers in terms of certain lifting data in characteristic p.

http://archive.numdam.org/article/ASENS_2003_4_36_1_113_0.pdf

Stefan Wewers

Papers

The local lifting problem for dihedral groups

Three point covers with bad reduction

Three point covers with bad reduction

Stable reduction of modular curves

Reduction and lifting of special metacyclic covers