Researcher:
Ünver, Sinan

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Researcher Of Publications: search.filters.isAuthorOfPublication.89d3c07d-a29c-425b-8ad3-a90cb72d45fe

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Now showing 1 - 10 of 16
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    Deformations of Bloch groups and Aomoto dilogarithms in characteristic p
    (Academic Press Inc Elsevier Science, 2011) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    In this paper, we study the Bloch group B-2(F[epsilon](2)) over the ring of dual numbers of the algebraic closure of the field with p elements, for a prime p >= 5. We show that a slight modification of Kontsevich's 11/2-logarithm defines a function on B-2(F[epsilon](2)). Using this function and the characteristic p version of the additive dilogarithm function that we previously defined, we determine the structure of the infinitesimal part of B-2(Ff[epsilon](2)) completely. This enables us to define invariants on the group of deformations of Aomoto dilogarithms and determine its structure. This final result might be viewed as the analog of Hilbert's third problem in characteristic p.
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    On the local unipotent fundamental group scheme
    (Canadian Science Publishing, 2010) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    We prove a local, unipotent, analog of Kedlaya's theorem for the pro-p part of the fundamental group of integral affine schemes in characteristic p.
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    Cyclotomic p-adic multi-zeta values in depth two
    (Springer Heidelberg, 2016) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    In this paper we compute the values of the p-adic multiple polylogarithms of depth two at roots of unity. Our method is to solve the fundamental differential equation satisfied by the crystalline frobenius morphism using rigid analytic methods. The main result could be thought of as a computation in the p-adic theory of higher cyclotomy. We expect the result to be useful in proving non-vanishing results since it gives quite explicit formulas.
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    On the purely irregular fundamental group
    (Wiley-V C H Verlag Gmbh, 2010) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    Based on the (not yet fully understood analogy) between irregular connections and wild ramification, we define a purely irregular fundamental group for complex algebraic varieties and prove some results about this fundamental group which are analogous to the p-adic etale fundamental group of algebraic varieties over fields of characteristic p.
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    Drinfelʼd–Ihara relations for p-adic multi-zeta values
    (Elsevier, 2013) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    We prove that the p-adic multi-zeta values satisfy the Drinfel'd-Ihara relations in Grothendieck-Teichmuller theory (Drinfel'd (1991) [10], Ihara (1991) [21]). This requires a detailed study of the crystalline theory of tangential basepoints in the higher dimensional case and Coleman integrals (Coleman (1982) [5]) as they relate to the frobenius invariant path of Vologodsky (2003) [31]. The main result (Theorem 1.8.1) is used in Furusho (2007) [14, pp. 1133-1135].
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    Motivic cohomology of fat points in Milnor range
    (Deutsche Mathematiker Vereinigung, 2018) Park, Jinhyun; Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials k[t]/(tm) in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the approaches via cycles with modulus. We prove that the groups in the Milnor range give the Milnor K-groups of k[t]/(tm), when the base field is of characteristic 0. Its relative part is the sum of the absolute Kähler differential forms.
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    On p-Adic periods for mixed tate motives over a number field
    (Int Press Boston, Inc, 2013) Chatzistamatiou, Andre; Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    For a number field, we have a Tannaka category of mixed Tate motives at our disposal. We construct p-adic points of the associated Tannaka group by using p-adic Hodge theory. Extensions of two Tate objects yield functions on the Tannaka group, and we show that evaluation at our p-adic points is essentially given by the inverse of the Bloch-Kato exponential map.
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    A note on the algebra of p-adic multi-zeta values
    (International Press of Boston, 2015) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    We prove that the algebra of p-adic multi-zeta values, as defined in [4] or [2], are contained in another algebra which is defined explicitly in terms of series. The main idea is to truncate certain series, expand them in terms of series all of which are divergent except one, and then take the limit of the convergent one. The main result is Theorem 3.12.
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    Swan conductors and torsion in the logarithmic de rham complex
    (Scientific Technical Research Council Turkey-Tubitak, 2010) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    We prove, for an arithmetic scheme X/S over a discrete valuation ring whose special fiber is a strict normal crossings divisor in X, that the Swan conductor of X/S is equal to the Euler characteristic of the torsion in the logarithmic de Rham complex of X/S This is a precise logarithmic analog of a theorem by Bloch [1].
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    A survey of the additive dilogarithm
    (Birkhauser, 2021) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    Borel’s construction of the regulator gives an injective map from the algebraic K–groups of a number field to its Deligne–Beilinson cohomology groups. This has many interesting arithmetic and geometric consequences. The formula for the regulator is expressed in terms of the classical polyogarithm functions. In this paper, we give a survey of the additive dilogarithm and the several different versions of the weight two regulator in the infinitesimal setting. We follow a historical approach which we hope will provide motivation for the definitions and the constructions.