The Scaling Site

We investigate the semi-ringed topos obtained by extension of scalars from the arithmetic site of our previous work, by replacing the smallest Boolean semifield by the tropical semifield of real numbers with the max-plus operations. The obtained site is the semi-direct product of the Euclidean half-line by the action of the monoid of positive integers by multiplication. Its points are the same as the points of the arithmetic site over the tropical semifield of real numbers, and coincide with the quotient of the adele class space of Q by the action of the maximal compact subgroup of the idele class group. The structure sheaf of the scaling topos endows it with a natural structure of tropical curve over the arithmetic topos. The restriction of this structure to the periodic orbits of the scaling flow gives, for each prime p, an analogue of an elliptic curve whose Jacobian is a cyclic group of order p-1. The Riemann-Roch formula holds and involves real valued dimensions and real degrees for divisors.Comment: 8 pages, minor typos and style corrected, notations clarified in v

The Arithmetic Site

We show that the non-commutative geometric approach to the Riemann zeta function has an algebraic geometric incarnation: the "Arithmetic Site". This site involves the tropical semiring viewed as a sheaf on the topos which is the dual of the multiplicative semigroup of positive integers. We prove that the set of points of the arithmetic site over the maximal compact subring of the tropical semifield is the non-commutative space quotient of the adele class space of Q by the action of the maximal compact subgroup of the idele class group. We realize the Frobenius correspondences in the square of the "Arithmetic Site" and compute their composition. This note provides the algebraic geometric space underlying the non-commutative approach to RH.Comment: 1 Figure, submitted to Comptes Rendu

41SM195A, The Browning Site

A surface collection of early 19th century historic sherds led to archeological investigations in 2002 and 2003 at the Browning site (41SM195A) in Smith County, Texas. My interest was whetted by mention in the original land abstract that the property had once been deeded to the Cherokee. In all, a total of 6.5 cubic meters was excavated, including twenty-two shovel tests and 10 1 x 1 m test units, and a fine-screen sample was taken from the midden. As a result, 1076 prehistoric and historic artifacts were recovered, along with new information about the Woodland period archeology in this part of East Texas. The initial shovel tests found, in addition to the historic component, a buried midden with evidence of Woodland period occupation. Based on the excavations, the midden covered approximately 500 m2. The 19th century historic artifacts were found in the upper sediment zone (a light brown sandy loam that was mostly gravel-free) covering the midden. The buried midden was a dark yellowish-brown gravelly loam that contained prehistoric pottery, bone, charred wood and nutshells, lithic materials, including lithic debris, flake tools, arrow and dart points, and ground stone tools. A calibrated radiocarbon date of AD 625 to 880 (2 sigma), with a calibrated intercept of AD 685, was obtained on charred nutshell from 40-50 cm bs in the midden zone. A series of Oxidizable Carbon Ratio dates from the midden indicate that the midden began to form about AD 147, with dates of AD 359-817 from the main part of the midden, indicating when the Browning site was most intensively occupied in prehistoric times

41SM195A, The Browning Site

A surface collection of early 19 \u27 century historic sherds led to archaeological investigations in 2002 and 2003 at the Browning site (41SM195A) in eastern Smith County, Texas. My interest was whetted by mention in the original land abstract that the property had once been deeded to the Cherokee Indians. In all, a total of 6.5 cubic meters of archaeological deposits was excavated at the site, including 22 shovel tests and 10 1 x 1 m test units, and fine-screen and flotation samples were taken from a prehistoric midden deposit identified during the work. As a result, 1075 prehistoric and historic artifacts were recovered, along with new information about Woodland period archaeology in this part of East Texas. The initial shovel tests found, in addition to the historic component, a buried midden with evidence of Woodland period occupation. Based on the excavations, the midden covered approximately 500 square meters. The 19th century historic artifacts were found in the upper sediment zone, a brown sandy loam that was mostly gravel- free) covering the midden. The buried midden was a dark yellowish-brown gravelly loam that contained prehistoric pottery, animal bone, charred wood and nutshells, lithic materials, including lithic debris, flake tools, arrow and dart points, and ground stone tools. A calibrated radiocarbon date of A.D. 625 to 880, with a calibrated intercept of A.D. 685, was obtained on charred nutshell from 40-50 em bs in the midden zone. A series of Oxidizable Carbon Ratio (OCR) dates from the midden indicate that the midden began to from about A.D. 147, with dates of A.D. 357-815 from the main part of the midden, indicating when the Browning site was most intensively occupied in prehistoric times

The Norman Site: Descriptions

The Norman site (34WG2) lay on a terrace on the west side of the Neosho (Grand) River in Wagoner County, Oklahoma. Throughout much of its course within Oklahoma, this river flows along the western boundary of the Ozark Uplift. East of the river, the limestones, shales, and sandstones deposited during the Upper Mississippian and Pennsylvanian geological periods form the Boston Mountains and the Springfield Plateau. Several of these formations contain knappable cherts, often of good quality. West of the river, the Mississippian and Pennsylvanian deposits thin and dip under the surface to form the Prairie Plains Province, characterized by low, east-facing escarpments. Sandstone and shale bedrocks underlie the Prairie-Plains Province. The streams flowing eastward across these are muddy and sluggish

The Overconvergent Site I. Coefficients

We define and study the overconvergent site of an algebraic variety, the sheaf of overconvergent functions on this site and show that the modules of finite presentations correspond to Berthelot's overconvergent isocrystals. We work with Berkovich theory instead of rigid analytic geometry and do not use any of Berthelot's results. This gives a complete alternative approach to rigid cohomology.Comment: 53 page

The Henry Chapman Site (41SM56)

In the mid-1950s, Sam Whiteside conducted excavations at the Henry Chapman site, his site P-5 (41SM56), on Prairie Creek in eastern Smith County, Texas, some 18 miles east of Tyler, Texas. Mr. Whiteside was an amateur archaeologist who discovered and explored numerous sites up and down Prairie Creek as well as other important sites in Smith and adjoining counties. The Chapman site was one of the first sites to be investigated by Mr. Whiteside, and the major part of the work took place there in 1957 and 1958. In August 1957, the site was visited by Edward B. Jelks and Leroy Johnson, who viewed the excavations and examined artifacts collected from there. Mr. Jelks, in notes on record at the Texas Archeological Research Laboratory (TARL) at The University of Texas in Austin, Texas, on August 21, 1958, indicated after observing the artifacts from the Henry Chapman site that the ceramics indicated an Alto focus occupation. He recognized Hickory Engraved and Holly Fine Engraved wares as well as Dunkin Incised and possible Pennington Punctated-Incised sherds. He mentioned that no Crockett Curvilinear Incised or Weches Fingernail Impressed sherds were present (two common types present at the Alto focus type site, the George C. Davis site [41CE19]). E. Mott Davis also visited the site in late 1957, and in February 1959, Davis, Lathel F. Duffield, and William A. Davis collected skeletal material from the site. In a June 15, 1958, newsletter from the East Texas Archeological Society (ETAS), Mr. Whiteside described excavations at the Henry Chapman site that had revealed refuse pits, post holes, and an abundance of pottery sherds indicative of an Alto focus occupation. In the summer of 1983, Mr. Whiteside visited the University of Texas Field School at the George C. Davis site, where he loaned some of his notes and collections from the Chapman site for recording purposes (these are on file at TARL). After Mr. Whiteside’s death, his family graciously allowed me access to his notes and artifacts. Not all of the artifacts have survived, having been stored in paper bags and subjected to several moves, but thanks to Mr. Whiteside’s writing lot numbers on artifacts and listing them in a journal, a majority of them have survived, and thus are suitable for study. Although 50 years have passed since Mr. Whiteside’s work at the Henry Chapman site, it is my intent to now make that work public

Covers of the arithmetic site

We give an explicit description of the Barr- and Diaconescu covers of the arithmetic site, which are relevant to cohomology. Further, we construct the arithmetic site as the commutative shadow of a non-commutative topological space