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

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Reflection Groups And Coxeter Groups

Modular elliptic curves and fermat's last theorem

Elements of mathematics

Algebraic number theory

Let F be a totally real field and p ≥ 3 a prime. If ρ : 
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is continuous, semisimple, totally odd, and tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which ρ is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which required p to be unramified in F. We also prove a theorem that verifies one half of the conjecture in many cases and use Dembele’s computations of Hilbert modular forms over \(\mathbb{Q}(\sqrt 5 )\) to provide evidence in support of the conjecture.

/pdf/weights-in-serre-s-conjecture-for-hilbert-modular-forms-the-2tr7j1vn85.pdf

Weights in serre's conjecture for hilbert modular forms: the ramified case

Let F be a totally real field and p an odd prime. If r is a continuous, semisimple, totally odd mod p representation of the absolute Galois group of F which is tamely ramified at all places of F dividing p, then we formulate a conjecture specifying the weights for which r is modular. This extends the conjecture of Diamond, Buzzard, and Jarvis, which supposed that p was unramified in F. We also prove a theorem towards the conjecture and provide some computational evidence.

Weights in Serre's conjecture for Hilbert modular forms: the ramified case

Let K be a number field with ring of integers OK . We compute the local factors of the normal zeta functions of the Heisenberg groups H(OK) at rational primes which are unramified in K. These factors are expressed as sums, indexed by Dyck words, of functions defined in terms of combinatorial objects such as weak orderings. We show that these local zeta functions satisfy functional equations upon the inversion of the prime.

/pdf/normal-zeta-functions-of-the-heisenberg-groups-over-number-1xod5qu7jn.pdf

Normal zeta functions of the Heisenberg groups over number rings I: the unramified case

Let F be a totally real field, p ≥ 3 a rational prime unramified in F , and p a place of F over p. Let ρ : Gal(F/F ) → GL2(Fp) be a two-dimensional mod p Galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible. We specify a set of weights, determined by the restriction of ρ to inertia at p, which contains all the modular weights for ρ. This proves part of a conjecture of Diamond, Buzzard, and Jarvis, which provides an analogue of Serre’s epsilon conjecture for Hilbert modular forms mod p.

/pdf/weights-of-galois-representations-associated-to-hilbert-166z00m54n.pdf

Weights of Galois representations associated to Hilbert modular forms

We compute explicitly the normal zeta functions of the Heisenberg groups H(R), where R is a compact discrete valuation ring of characteristic zero. These zeta functions occur as Euler factors of normal zeta functions of Heisenberg groups of the form H(O
 K
 ), where O
 K
 is the ring of integers of an arbitrary number field K, at the rational primes which are non-split in K. We show that these local zeta functions satisfy functional equations upon inversion of the prime.

/pdf/normal-zeta-functions-of-the-heisenberg-groups-over-number-33c5ka28an.pdf

Michael M. Schein

Papers

Weights in serre's conjecture for hilbert modular forms: the ramified case

Weights in Serre's conjecture for Hilbert modular forms: the ramified case

Normal zeta functions of the Heisenberg groups over number rings I: the unramified case

Weights of Galois representations associated to Hilbert modular forms

Normal zeta functions of the Heisenberg groups over number rings II — the non-split case